EDA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "512ecc43",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hadoop/miniconda/lib/python3.7/site-packages/dask_yarn/core.py:16: FutureWarning: format_bytes is deprecated and will be removed in a future release. Please use dask.utils.format_bytes instead.\n",
      "  from distributed.utils import (\n",
      "/home/hadoop/miniconda/lib/python3.7/site-packages/dask_yarn/core.py:16: FutureWarning: parse_timedelta is deprecated and will be removed in a future release. Please use dask.utils.parse_timedelta instead.\n",
      "  from distributed.utils import (\n"
     ]
    }
   ],
   "source": [
    "from dask_yarn import YarnCluster\n",
    "from dask.distributed import Client\n",
    "import dask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50942b07",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "distributed.scheduler - INFO - Clear task state\n",
      "distributed.scheduler - INFO -   Scheduler at: tcp://172.31.25.252:40861\n",
      "distributed.scheduler - INFO -   dashboard at:                    :35941\n",
      "distributed.scheduler - INFO - Receive client connection: Client-30fe7718-5a22-11ec-8cbe-0ad7bf2eb063\n",
      "distributed.core - INFO - Starting established connection\n"
     ]
    }
   ],
   "source": [
    "# Create a cluster where each worker has 4 vCPU core and 8 GiB of memory:\n",
    "cluster = YarnCluster(environment=\"/home/hadoop/environment.tar.gz\",\n",
    "                      worker_vcores = 4,\n",
    "                      worker_memory = \"8GiB\"\n",
    "                      )\n",
    "\n",
    "# Scale cluster out to 2 such workers:\n",
    "cluster.scale(2)\n",
    "\n",
    "# Connect to the cluster (before proceeding, you should wait for workers to be registered by the dask scheduler, as below):\n",
    "client = Client(cluster)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fbc424fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "    <div style=\"width: 24px; height: 24px; background-color: #e1e1e1; border: 3px solid #9D9D9D; border-radius: 5px; position: absolute;\"> </div>\n",
       "    <div style=\"margin-left: 48px;\">\n",
       "        <h3 style=\"margin-bottom: 0px;\">Client</h3>\n",
       "        <p style=\"color: #9D9D9D; margin-bottom: 0px;\">Client-30fe7718-5a22-11ec-8cbe-0ad7bf2eb063</p>\n",
       "        <table style=\"width: 100%; text-align: left;\">\n",
       "\n",
       "        <tr>\n",
       "        \n",
       "            <td style=\"text-align: left;\"><strong>Connection method:</strong> Cluster object</td>\n",
       "            <td style=\"text-align: left;\"><strong>Cluster type:</strong> dask_yarn.YarnCluster</td>\n",
       "        \n",
       "        </tr>\n",
       "\n",
       "        \n",
       "            <tr>\n",
       "                <td style=\"text-align: left;\">\n",
       "                    <strong>Dashboard: </strong> <a href=\"/proxy/35941/status\" target=\"_blank\">/proxy/35941/status</a>\n",
       "                </td>\n",
       "                <td style=\"text-align: left;\"></td>\n",
       "            </tr>\n",
       "        \n",
       "\n",
       "        </table>\n",
       "\n",
       "        \n",
       "            <details>\n",
       "            <summary style=\"margin-bottom: 20px;\"><h3 style=\"display: inline;\">Cluster Info</h3></summary>\n",
       "            <div style='background-color: #f2f2f2; display: inline-block; padding: 10px; border: 1px solid #999999;'>\n",
       "  <h3>YarnCluster</h3>\n",
       "  <ul>\n",
       "    <li><b>Application ID: </b>application_1639177101437_0003\n",
       "    <li><b>Dashboard: </b><a href='/proxy/35941/status' target='_blank'>/proxy/35941/status</a>\n",
       "  </ul>\n",
       "</div>\n",
       "\n",
       "            </details>\n",
       "        \n",
       "\n",
       "    </div>\n",
       "</div>"
      ],
      "text/plain": [
       "<Client: 'tcp://172.31.25.252:40861' processes=0 threads=0, memory=0 B>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "client"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ed2160e",
   "metadata": {},
   "source": [
    "### Data loading using dask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2cd55cf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import dask.dataframe as dd\n",
    "df = dd.read_csv(\"s3://yijingzhang-bucket/train.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7bd7bc76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['row_id', 'timestamp', 'user_id', 'content_id', 'content_type_id',\n",
       "       'task_container_id', 'user_answer', 'answered_correctly',\n",
       "       'prior_question_elapsed_time', 'prior_question_had_explanation'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bdcbae2a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "row_id                              int64\n",
      "timestamp                           int64\n",
      "user_id                             int64\n",
      "content_id                          int64\n",
      "content_type_id                     int64\n",
      "task_container_id                   int64\n",
      "user_answer                         int64\n",
      "answered_correctly                  int64\n",
      "prior_question_elapsed_time       float64\n",
      "prior_question_had_explanation     object\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.options.display.max_rows =99\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b0fb3f3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'dask.dataframe.core.DataFrame'>\n",
      "Columns: 10 entries, row_id to prior_question_had_explanation\n",
      "dtypes: object(1), float64(1), int64(8)"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "64095095",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "distributed.scheduler - INFO - Register worker <WorkerState 'tcp://172.31.26.25:35837', name: dask.worker_0, status: undefined, memory: 0, processing: 0>\n",
      "distributed.scheduler - INFO - Starting worker compute stream, tcp://172.31.26.25:35837\n",
      "distributed.core - INFO - Starting established connection\n",
      "distributed.scheduler - INFO - Register worker <WorkerState 'tcp://172.31.26.183:38973', name: dask.worker_1, status: undefined, memory: 0, processing: 0>\n",
      "distributed.scheduler - INFO - Starting worker compute stream, tcp://172.31.26.183:38973\n",
      "distributed.core - INFO - Starting established connection\n"
     ]
    },
    {
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       "      <th>row_id</th>\n",
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       "      <th>user_id</th>\n",
       "      <th>content_id</th>\n",
       "      <th>content_type_id</th>\n",
       "      <th>task_container_id</th>\n",
       "      <th>user_answer</th>\n",
       "      <th>answered_correctly</th>\n",
       "      <th>prior_question_elapsed_time</th>\n",
       "      <th>prior_question_had_explanation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
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       "      <td>115</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>11000.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   row_id  timestamp  user_id  content_id  content_type_id  task_container_id  \\\n",
       "0       0          0      115        5692                0                  1   \n",
       "1       1      56943      115        5716                0                  2   \n",
       "2       2     118363      115         128                0                  0   \n",
       "3       3     131167      115        7860                0                  3   \n",
       "4       4     137965      115        7922                0                  4   \n",
       "\n",
       "   user_answer  answered_correctly  prior_question_elapsed_time  \\\n",
       "0            3                   1                          NaN   \n",
       "1            2                   1                      37000.0   \n",
       "2            0                   1                      55000.0   \n",
       "3            0                   1                      19000.0   \n",
       "4            1                   1                      11000.0   \n",
       "\n",
       "  prior_question_had_explanation  \n",
       "0                            NaN  \n",
       "1                          False  \n",
       "2                          False  \n",
       "3                          False  \n",
       "4                          False  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "458f7467",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique content IDs: 13782\n",
      "Unique task container IDs: 10000\n",
      "Number of content types: 2\n"
     ]
    }
   ],
   "source": [
    "# Calling dask.compute() with multiple objects allows for shared computation steps, e.g., file loading, and reduces overall runtime\n",
    "num_content_ids, num_task_ids, num_content_types = dask.compute(df['content_id'].nunique(),\\\n",
    "                                                               df['task_container_id'].nunique(),\\\n",
    "                                                               df['content_type_id'].nunique())\n",
    "print(\"Unique content IDs: {}\".format(num_content_ids))\n",
    "print(\"Unique task container IDs: {}\".format(num_task_ids))\n",
    "print(\"Number of content types: {}\".format(num_content_types))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "890bac50",
   "metadata": {},
   "source": [
    "### How many users in total?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a8ac2749",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of users: 393656\n"
     ]
    }
   ],
   "source": [
    "print(\"Total number of users: {}\".format(df['user_id'].nunique().compute()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e023c27",
   "metadata": {},
   "source": [
    "### The proportion of correct answers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "94c50eec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct rate of all answers: 65.72%\n"
     ]
    }
   ],
   "source": [
    "print(\"Correct rate of all answers: {:.2f}%\".format(df[df['content_type_id']==0]['answered_correctly'].mean().compute() * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6c17c79",
   "metadata": {},
   "source": [
    "### Explore the questions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a659a3ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Aggregating at the content (question) level\n",
    "content_df = (df.query(\"content_type_id==0\")\n",
    "              .groupby('content_id')\n",
    "              .agg({'user_id': 'count',\n",
    "                    'answered_correctly': 'mean'})\n",
    "              .compute())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b5f59ad7",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <td>6903</td>\n",
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       "      <th>10008</th>\n",
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       "      <td>1.000000</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>13523 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            user_id  answered_correctly\n",
       "content_id                             \n",
       "0              6903            0.907721\n",
       "1              7398            0.890646\n",
       "2             44905            0.554281\n",
       "3             22973            0.779437\n",
       "4             31736            0.613215\n",
       "...             ...                 ...\n",
       "5823              1            1.000000\n",
       "10005             1            1.000000\n",
       "10006             1            1.000000\n",
       "10007             1            0.000000\n",
       "10008             1            1.000000\n",
       "\n",
       "[13523 rows x 2 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "content_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "39e363ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_ques = pd.read_csv(\"questions.csv\") # the question data is small data, so we don't need the Dask to read it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7df378b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 13523 entries, 0 to 13522\n",
      "Data columns (total 5 columns):\n",
      " #   Column          Non-Null Count  Dtype \n",
      "---  ------          --------------  ----- \n",
      " 0   question_id     13523 non-null  int64 \n",
      " 1   bundle_id       13523 non-null  int64 \n",
      " 2   correct_answer  13523 non-null  int64 \n",
      " 3   part            13523 non-null  int64 \n",
      " 4   tags            13522 non-null  object\n",
      "dtypes: int64(4), object(1)\n",
      "memory usage: 528.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df_ques.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1d4055e7",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
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       "      <th>bundle_id</th>\n",
       "      <th>correct_answer</th>\n",
       "      <th>part</th>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>131 101 162 92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>131 149 162 29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>131 5 162 38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   question_id  bundle_id  correct_answer  part            tags\n",
       "0            0          0               0     1   51 131 162 38\n",
       "1            1          1               1     1       131 36 81\n",
       "2            2          2               0     1  131 101 162 92\n",
       "3            3          3               0     1  131 149 162 29\n",
       "4            4          4               3     1    131 5 162 38"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ques.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01ca298",
   "metadata": {},
   "source": [
    "#### The number of unique parts "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "522f6d65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of unique parts: 7\n"
     ]
    }
   ],
   "source": [
    "print(\"The number of unique parts: {}\".format(df_ques['part'].nunique()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7c7a9a7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# merge questions.csv with aggregate content dataframe\n",
    "content_df = (content_df.reset_index().rename(columns={\"content_id\": \"question_id\"})\n",
    "              .merge(df_ques, how='left', on=['question_id']))\n",
    "content_df['num_answered_correctly'] = (content_df['user_id'] * content_df['answered_correctly']).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5d965d29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>question_id</th>\n",
       "      <th>user_id</th>\n",
       "      <th>answered_correctly</th>\n",
       "      <th>bundle_id</th>\n",
       "      <th>correct_answer</th>\n",
       "      <th>part</th>\n",
       "      <th>tags</th>\n",
       "      <th>num_answered_correctly</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>6903</td>\n",
       "      <td>0.907721</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>51 131 162 38</td>\n",
       "      <td>6266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>7398</td>\n",
       "      <td>0.890646</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>131 36 81</td>\n",
       "      <td>6589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>44905</td>\n",
       "      <td>0.554281</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>131 101 162 92</td>\n",
       "      <td>24890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>22973</td>\n",
       "      <td>0.779437</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>131 149 162 29</td>\n",
       "      <td>17906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>31736</td>\n",
       "      <td>0.613215</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>131 5 162 38</td>\n",
       "      <td>19461</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   question_id  user_id  answered_correctly  bundle_id  correct_answer  part  \\\n",
       "0            0     6903            0.907721          0               0     1   \n",
       "1            1     7398            0.890646          1               1     1   \n",
       "2            2    44905            0.554281          2               0     1   \n",
       "3            3    22973            0.779437          3               0     1   \n",
       "4            4    31736            0.613215          4               3     1   \n",
       "\n",
       "             tags  num_answered_correctly  \n",
       "0   51 131 162 38                    6266  \n",
       "1       131 36 81                    6589  \n",
       "2  131 101 162 92                   24890  \n",
       "3  131 149 162 29                   17906  \n",
       "4    131 5 162 38                   19461  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "content_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e3d74d0",
   "metadata": {},
   "source": [
    "#### Are each questions attempted for similar times? Which could reflect the diffculty level of the question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9e239086",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: seaborn in ./miniconda/lib/python3.7/site-packages (0.11.2)\n",
      "Requirement already satisfied: pandas>=0.23 in ./miniconda/lib/python3.7/site-packages (from seaborn) (1.3.1)\n",
      "Requirement already satisfied: numpy>=1.15 in ./miniconda/lib/python3.7/site-packages (from seaborn) (1.21.1)\n",
      "Requirement already satisfied: scipy>=1.0 in ./miniconda/lib/python3.7/site-packages (from seaborn) (1.7.3)\n",
      "Requirement already satisfied: matplotlib>=2.2 in ./miniconda/lib/python3.7/site-packages (from seaborn) (3.5.0)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (4.25.0)\n",
      "Requirement already satisfied: packaging>=20.0 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (21.3)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (1.3.1)\n",
      "Requirement already satisfied: cycler>=0.10 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (0.11.0)\n",
      "Requirement already satisfied: pillow>=6.2.0 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (8.3.1)\n",
      "Requirement already satisfied: pyparsing>=2.2.1 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (3.0.6)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in ./miniconda/lib/python3.7/site-packages (from matplotlib>=2.2->seaborn) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2017.3 in ./miniconda/lib/python3.7/site-packages (from pandas>=0.23->seaborn) (2021.3)\n",
      "Requirement already satisfied: six>=1.5 in ./miniconda/lib/python3.7/site-packages (from python-dateutil>=2.7->matplotlib>=2.2->seaborn) (1.16.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b4158664",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cb6ef9c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(content_df['user_id'].sort_values(ascending=False).values)\n",
    "plt.yscale(\"log\")\n",
    "plt.title(\"Number of attempts & Questions\")\n",
    "plt.xlabel(\"Questions\")\n",
    "plt.ylabel(\"Number of attempts\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "336a6017",
   "metadata": {},
   "source": [
    "### Are the difficulty of the questions varying?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "77259ae8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdQklEQVR4nO3de5RcZZnv8e+PBEOkMYDBniREGgUvQAYGWnRGZ6YjjlycWdFZ6sThKFE0XhgvY+Yc4mUOLDUDniMyF2QgGhYoSptBlIjiiIxt9EhE4kKbgGiEGJJgIhACjYiT+Jw/9pv0TqcqVd1V1VX99u+zVq3e9e7bs9/a+6l3v3vXbkUEZmaWlwPaHYCZmTWfk7uZWYac3M3MMuTkbmaWISd3M7MMObmbmWXIyX2MJF0h6R+btKxnSxqSNCW9H5D01mYsOy3vZknnNGt5o1jvxyQ9JOlX471uaw1JL5X087S/vrrd8VQy8niarJzcK5C0QdKTkh6X9Kik70t6h6Q99RUR74iIj9a5rFfsb5qI2BgRXRGxqwmxXyjp2hHLPzMirml02aOMYy6wBDguIv5gPNc9VpJ6JIWkqe2OZawk9Una1MJVfAS4LO2vX2nheuo28hhr5vE0kTm5V/dXEXEIcBRwMXA+sKLZK5nIiaSGo4CHI2JbK1cysv5UyHK/7pBtOwpY1+YYrB4R4deIF7ABeMWIslOB3wMnpPdXAx9LwzOBm4BHgUeA71J8cX4uzfMkMAT8L6AHCOBcYCOwulQ2NS1vALgIuB3YAdwIHJ7G9QGbKsULnAH8DvjvtL4fl5b31jR8APBh4JfANuCzwIw0bncc56TYHgI+tJ96mpHm/3Va3ofT8l+Rtvn3KY6rq8y/ALgTeAz4BXBGKp8NrEp1uR54W2meC4HrgWvTfG9N27cM+H9pvccALwBuScu4F3h9aRnTgUtSzDuA76WyjWn7h9Lrj4FFafwngO3A/cCZI+pgBfAgsBn4GDAljTsG+E5ax0PAF1O5gEtT/e8AfkLaryrUUaVtezNwD/A4cB/w9jTtwSPqfSjV5QHA0lTHDwMrSftTlXW+LdX7I+lzmJ3Kf8He+/O0CvP+EfCjFNsXgX6Gj5NFwPdGTB/AMWl4WqrnjcBW4ApgegPH2NQ696eVFPvx4xRfXL2l8eenz/Vxiv3otHbnp7rzWLsD6MQXFZJ7Kt8IvDMNX13aaS9KO+KB6fWngCotq7TjfTYdjNMr7IwDaYc6IU3zJeDaNK6PKsm9tLNeO2L8AMPJ/S1pB38O0AXcAHxuRGyfTnGdCDwFvLBKPX2W4ovnkDTvz4Bzq8U5Yt5TKRLbX6SDdA7wgjTuO8DlwEHASRRfHqeVtu+/gVen+aan7dsIHA9MpUi4D1AkwanAyRTJ9fi0jE+leeYAU4A/oUgse30OadpFaX1vS9O+E9hS+ny/AlyZPqdnUXwh70621wEfSnEeBLwslZ8OrAUOpUj0LwRmVamnkdt2IPAq4Llp3j8HfgOcvJ/9433AGuDItJ1XAtdVWd/LU12dnKb9N2B1rWMjjXsaxRfm36c4X5vqrt7k/s8USfhwin3qq8BFDRxju4+nWvvTb4Gz0ud7EbAmjXs+xX40u7Tc57Y7P9Wdx9odQCe+qu3A6QD5UBq+urTTfoQiyR1Ta1mlHe85FcrKyf3i0vjjKFrkU6ocvHvWQe3kfivwrtK456cDcGopjiNL428HFlbYrikUif+4UtnbgYE0vE+cI+a/Eri0QvlcYBdwSKnsIlLrP23f6grb95HS+78BvlthfRdQJNongRMrrHuvzyGVLQLWl94/PU3zB0B3qoPppfFvAL6dhj8LLC/XZyp/OcUX4UuAA2rsi3ttW5VpvgK8t1q9U7TyTyu9n7X7M6+wrBXA/ym970rT9uzv2Ejj/ozSF18q+z51JHeKL6onKCVPijOn+xs4xqbWuT99a8Sx9mQaPobi7OoVwIH7+ww68dXu/ruJZg7Fqd1I/5eiNfxNSfdJWlrHsh4YxfhfUrRWZtYV5f7NTssrL3sqRaLarXx3y28oDvCRZjLcUisva06dccylOM2vFN8jEfH4fpZbqe7KZUcBL04Xwx+V9ChwNkVCnknRgqu07mr21EdE/CYNdqX1HAg8WFrPlRQteCi6CATcLmmdpLekZfwXcBnFGcRWScslPWM/699reyWdKWmNpEfSOs9i//vGUcCXSzHeQ5HwuitMu9f+ERFDFF059Xyus4HNkTJj8stqE49wBMUX59pSnN9I5TC2Y2x3TLX2p5H7+0GSpkbEeoqznguBbZL6Jc2uc71t5+ReJ0kvotghvjdyXEQ8HhFLIuI5wF8B75d02u7RVRZZrXy3uaXhZ1O0nh6iaN08vRTXFIYPgHqWu4XiYC8veydFH+doPJRiGrmszXXO/wBF10Kl+A6XdMh+lltpG8tlDwDfiYhDS6+uiHhnivu3VdZdq+5GeoCi5T6ztJ5nRMTxABHxq4h4W0TMpjiruVzSMWncv0bEKRTdLc8D/ud+1rMnLknTKLrpPgF0R8ShwNcpvkSqbcMDFNcJyvVxUERU+qz22j8kHQw8k/o+1weBOZJUKnt2aXjkvlu+i+ohijOq40sxzoiILhjzMbZ7e2rtT1VFxBci4mUUdRLAx+uZrxM4udcg6RmS/pLiwtC1ETFYYZq/lHRM2qkfo2gV7b4NaytF//Zo/Q9Jx0l6OsUp6fVR3Nr1M4qWxaskHUhxEXNaab6tQM9+7qq4Dvh7SUdL6gL+ieJC387RBJdiWQksk3SIpKOA91Nc6KzHCuDNkk6TdICkOZJeEBEPUJzKXyTpIEl/SHHx+fOjCO8m4HmS3ijpwPR6kaQXRsTvgauAT0qaLWmKpD9OSfPXFBfn6vq8IuJB4JvAJWk/OUDScyX9OYCk10k6Mk2+nSI57EqxvDh9fk9QfNnUe9ve0yg+718DOyWdCbyyNH4r8ExJM0plV1B8TkeluI6QtKDK8r9A8bmclOrkn4AfRMSGOmK7jaKh8B5JUyX9NcW1ld1+DByfln0QRYsYgPS5fBq4VNKzUpxzJJ2ehsd0jDWyP0l6vqSXp3r4LcWXz4S5vdLJvbqvSnqcotXzIeCTFBfoKjkW+BbF1frbgMsjYiCNuwj4cDrV/IdRrP9zFP36v6LoRngPQETsAN4FfIai9fEEUL6v+T/S34cl/ajCcq9Ky15NcefHb4F3jyKusnen9d9HcUbzhbT8miLidor6vJTiwup3GG4xvoGi33QL8GXggoi4pd6g0in4K4GFaRm/omhx7f4S/AdgEPghRTfbxyn6vn9DujMlfV4vqWN1b6JIuHdTJPDrKfq0AV4E/EDSEMWFwvdGxP3AMygS2XaKLoKHKVri9W7beyi+WLcDf5uWvXv8Tym+wO9L2zAb+Jc0zTfTPr0GeHGV5d8K/CPF2cGDFGc4C+uM7XfAX1P0rW+nuPZxQ2n8zygaKt8Cfs6+Z8HnU3S9rJH0WJru+WlcI8fYWPenaRS3QT9EsQ89C/hgHfN1hN1Xm83Mmk7S1RQXeD/c7lgmG7fczcwy5ORuZpYhd8uYmWXILXczswx1xEOrZs6cGT09Pe0Oo2meeOIJDj744HaH0RFcF8NcF8NcF8MaqYu1a9c+FBFHVBrXEcm9p6eHO+64o91hNM3AwAB9fX3tDqMjuC6GuS6GuS6GNVIXkqr+AtjdMmZmGXJyNzPLkJO7mVmGnNzNzDLk5G5mliEndzOzDDm5m5llyMndzCxDTu5mZhnqiF+omtnE07P0a3uGN1z8qjZGYpW45W5mliEndzOzDDm5m5llyMndzCxDTu5mZhlycjczy5CTu5lZhpzczcwy5ORuZpYh/0LVzBrmX6t2Hrfczcwy5ORuZuNucPMOepZ+ba8WvzWXk7uZWYZq9rlLOghYDUxL018fERdIOhz4ItADbABeHxHb0zwfAM4FdgHviYj/bEn0ZpYt9+M3pp6W+1PAyyPiROAk4AxJLwGWArdGxLHArek9ko4DFgLHA2cAl0ua0oLYzcysipot94gIYCi9PTC9AlgA9KXya4AB4PxU3h8RTwH3S1oPnArc1szAzazzufXdPipyd42Jipb3WuAY4FMRcb6kRyPi0NI02yPiMEmXAWsi4tpUvgK4OSKuH7HMxcBigO7u7lP6+/ubtU1tNzQ0RFdXV7vD6Aiui2G51cXg5h0Vy+fNmVFxmnL5tkd2sPXJfcurLb/aNDloZL+YP3/+2ojorTSurvvcI2IXcJKkQ4EvSzphP5Or0iIqLHM5sBygt7c3+vr66gllQhgYGCCn7WmE62JYbnWxqMqdLhvO7qs4Tbn83z5/I5cMTt2nvOryB58YXk5mZwCt2i9G9SOmiHhU0gBFX/pWSbMi4kFJs4BtabJNwNzSbEcCW5oRrJm1l29dnDhqXlCVdERqsSNpOvAK4KfAKuCcNNk5wI1peBWwUNI0SUcDxwK3NzluMzPbj3pa7rOAa1K/+wHAyoi4SdJtwEpJ5wIbgdcBRMQ6SSuBu4GdwHmpW8fMJoFGWvc+M2ieeu6W+QnwRxXKHwZOqzLPMmBZw9GZmdmY+BeqZmYZ8lMhzWy/Wt1V4q6Y1nByN7NxUU7iS+a1MZBJwt0yZmYZcnI3M8uQu2XMDPBzYHLj5G42ifliZr7cLWNmliG33M1sQnH3UX3ccjczy5CTu5lZhtwtY2b7mIgXWt1dszcndzObsCbil9B4cbeMmVmGnNzNzDLk5G5mliH3uZtlzhcaJye33M3MMuTkbmaWIXfLmFl23BXllruZWZac3M3MMlQzuUuaK+nbku6RtE7Se1P5hZI2S7ozvc4qzfMBSesl3Svp9FZugJmZ7auePvedwJKI+JGkQ4C1km5J4y6NiE+UJ5Z0HLAQOB6YDXxL0vMiYlczAzez0fPP9SePmsk9Ih4EHkzDj0u6B5izn1kWAP0R8RRwv6T1wKnAbU2I18yq8EVEK1NE1D+x1AOsBk4A3g8sAh4D7qBo3W+XdBmwJiKuTfOsAG6OiOtHLGsxsBigu7v7lP7+/oY3plMMDQ3R1dXV7jA6gutiWKvrYnDzjj3D8+bMqFjeKbqnw9Ynx2dd5broRI3sF/Pnz18bEb2VxtV9K6SkLuBLwPsi4jFJ/w58FIj09xLgLYAqzL7PN0hELAeWA/T29kZfX1+9oXS8gYEBctqeRrguhrWiLvbuZhk+nDecPbyeRR3YFbNk3k4uGRyfO7HLddGJWnWM1FW7kg6kSOyfj4gbACJia2n8p4Gb0ttNwNzS7EcCW5oSrZlZAyZT11U9d8sIWAHcExGfLJXPKk32GuCuNLwKWChpmqSjgWOB25sXspmZ1VJPy/2lwBuBQUl3prIPAm+QdBJFl8sG4O0AEbFO0krgboo7bc7znTJm1i6T9Q6heu6W+R6V+9G/vp95lgHLGojLzMwa4F+ompllyA8OM5tgJms3g42OW+5mZhlyy90sQ27dm1vuZmYZcnI3M8uQk7uZWYac3M3MMuTkbmaWISd3M7MMObmbmWXIyd3MLENO7mZmGfIvVM061GT6xxLWfG65m5llyC13swnAz4qx0XLL3cwsQ07uZmYZcnI3M8uQ+9zNOoj71q1Z3HI3M8uQk7uZWYbcLWPWBu5+ab/cfyRWs+Uuaa6kb0u6R9I6Se9N5YdLukXSz9Pfw0rzfEDSekn3Sjq9lRtgZmb7qqflvhNYEhE/knQIsFbSLcAi4NaIuFjSUmApcL6k44CFwPHAbOBbkp4XEbtaswlmZo0ZeSaVQ0u+Zss9Ih6MiB+l4ceBe4A5wALgmjTZNcCr0/ACoD8inoqI+4H1wKlNjtvMzPZDEVH/xFIPsBo4AdgYEYeWxm2PiMMkXQasiYhrU/kK4OaIuH7EshYDiwG6u7tP6e/vb3BTOsfQ0BBdXV3tDqMjuC6GleticPOONkfTXt3TYeuT7Y6iunlzZozbuho5RubPn782Inorjav7gqqkLuBLwPsi4jFJVSetULbPN0hELAeWA/T29kZfX1+9oXS8gYEBctqeRrguhpXrYtEkv6C6ZN5OLhns3Ps5NpzdN27ratUxUtetkJIOpEjsn4+IG1LxVkmz0vhZwLZUvgmYW5r9SGBLc8I1M7N61HO3jIAVwD0R8cnSqFXAOWn4HODGUvlCSdMkHQ0cC9zevJDNzKyWes6LXgq8ERiUdGcq+yBwMbBS0rnARuB1ABGxTtJK4G6KO23O850yZmbjq2Zyj4jvUbkfHeC0KvMsA5Y1EJeZmTWgc69omJl1gIn6S1Ynd7NxMrh5x6S/S8bGjx8cZmaWISd3M7MMObmbmWXIyd3MLENO7mZmGfLdMmYtVL6Nbsm8NgZio5LDP1Nxy93MLENO7mZmGXJyNzPLkJO7mVmGnNzNzDLk5G5mliEndzOzDDm5m5llyD9iMmuCifrMb8uXW+5mZhlycjczy5C7ZcyaLIfnktjE55a7mVmGnNzNzDLk5G5mlqGayV3SVZK2SbqrVHahpM2S7kyvs0rjPiBpvaR7JZ3eqsDN2qFn6df2vMw6WT0t96uBMyqUXxoRJ6XX1wEkHQcsBI5P81wuaUqzgjUzs/rUTO4RsRp4pM7lLQD6I+KpiLgfWA+c2kB8ZmY2BoqI2hNJPcBNEXFCen8hsAh4DLgDWBIR2yVdBqyJiGvTdCuAmyPi+grLXAwsBuju7j6lv7+/GdvTEYaGhujq6mp3GB0ht7oY3Lxjz/C8OTMqllfTPR22PtmSsCaciVoX5c+8WRo5RubPn782InorjRvrfe7/DnwUiPT3EuAtgCpMW/HbIyKWA8sBent7o6+vb4yhdJ6BgQFy2p5G5FYXi8qPGTi7r2J5NUvm7eSSQf+0BCZwXQw+sWewWY+ZaNUxMqbajYitu4clfRq4Kb3dBMwtTXoksGXM0Zl1MF9UtU42plshJc0qvX0NsPtOmlXAQknTJB0NHAvc3liIZmY2WjVb7pKuA/qAmZI2ARcAfZJOouhy2QC8HSAi1klaCdwN7ATOi4hdLYnczMyqqpncI+INFYpX7Gf6ZcCyRoIyM7PG+BeqZmYZcnI3M8uQk7uZWYac3M3MMuTkbmaWoQn4EzGz1vM/vLaJzi13M7MMueVuZjYGnX525+RuVoOfIWMTkZO7WeIkbjlxn7uZWYac3M3MMuRuGZvU3BVjuXLL3cwsQ07uZmYZcreMTQrufrHJxi13M7MMueVuWXJL3SY7t9zNzDLk5G5mliEndzOzDLnP3Sa0Tn8yn1m71Gy5S7pK0jZJd5XKDpd0i6Sfp7+HlcZ9QNJ6SfdKOr1VgZuZdYqepV/b8+oU9XTLXA2cMaJsKXBrRBwL3JreI+k4YCFwfJrncklTmhatmZnVpWa3TESsltQzongB0JeGrwEGgPNTeX9EPAXcL2k9cCpwW5PiNeuo1pFZp1JE1J6oSO43RcQJ6f2jEXFoafz2iDhM0mXAmoi4NpWvAG6OiOsrLHMxsBigu7v7lP7+/iZsTmcYGhqiq6ur3WF0hFbUxeDmHRXL582ZUXOaduqeDlufbHcUnSHnuijvh/Vo5BiZP3/+2ojorTSu2RdUVaGs4rdHRCwHlgP09vZGX19fk0Npn4GBAXLanka0oi4WVWm5bzi7r+Y07bRk3k4uGfQ9DJB3XZT3w3q0Kl+M9VbIrZJmAaS/21L5JmBuabojgS1jD8/MzMZirMl9FXBOGj4HuLFUvlDSNElHA8cCtzcWopmZjVbN8yJJ11FcPJ0paRNwAXAxsFLSucBG4HUAEbFO0krgbmAncF5E7GpR7GZmVkU9d8u8ocqo06pMvwxY1khQZmbWmDyvaFh2fPuj2ej42TJmZhlyy93MrEXa+ewjt9zNzDLk5G5mliF3y1g2fNHVbJhb7mZmGXJyNzPLkLtlzMyaqFO6B91yNzPLkFvu1rE6pQVkNhG55W5mliG33K2juLVu1hxO7tYU7fyZtZnty90yZmYZcnI3M8uQk7uZWYbc527jxv3yZuPHLXczsww5uZuZZcjdMtZ2vrfdrPmc3K0tnNDNWsvJ3UbFF0XNJoaGkrukDcDjwC5gZ0T0Sjoc+CLQA2wAXh8R2xsL08zMRqMZF1TnR8RJEdGb3i8Fbo2IY4Fb03szMxtHrbhbZgFwTRq+Bnh1C9ZhZmb7oYgY+8zS/cB2IIArI2K5pEcj4tDSNNsj4rAK8y4GFgN0d3ef0t/fP+Y4Os3Q0BBdXV3tDqMlBjfvGNX03dNh65MtCmaCcV0Mm4x1MW/OjIrljeSL+fPnry31muyl0QuqL42ILZKeBdwi6af1zhgRy4HlAL29vdHX19dgKJ1jYGCAnLZn7ztbRrfLLJm3k0sGfd0eXBdlk7EuNpzdV7G8VfmioW6ZiNiS/m4DvgycCmyVNAsg/d3WaJBmZjY6Y07ukg6WdMjuYeCVwF3AKuCcNNk5wI2NBmlmZqPTyHlRN/BlSbuX84WI+IakHwIrJZ0LbARe13iYZmY2GmNO7hFxH3BihfKHgdMaCcrawz9QMsuHHxxmZpYhJ3czswxNrnuRbB9+gJdZntxyNzPLkFvuk8RoL5a6RW82sTm5T0JO3Gb5c7eMmVmG3HLPmFvoZpOXk/sEUa3P3AncbGIY7x8JulvGzCxDTu5mZhlycjczy5CTu5lZhnxBdRw164KKL6KaWS1uuZuZZcgt9zbxs9PNrJWc3FuskS4Ud7+Y2Vi5W8bMLENuuXcAd9GYTS7lY/7qMw5uyTqc3DuMu2LMrBmc3JuknJSXzNvJIidpM2sjJ/cGuJVtZp3KF1TNzDLUspa7pDOAfwGmAJ+JiItbta7x5Na6mU0ELUnukqYAnwL+AtgE/FDSqoi4uxXraxY/M93MctGqlvupwPqIuA9AUj+wAGhJcm/FP392QjeziUwR0fyFSq8FzoiIt6b3bwReHBF/V5pmMbA4vX0+cG/TA2mfmcBD7Q6iQ7guhrkuhrkuhjVSF0dFxBGVRrSq5a4KZXt9i0TEcmB5i9bfVpLuiIjedsfRCVwXw1wXw1wXw1pVF626W2YTMLf0/khgS4vWZWZmI7Qquf8QOFbS0ZKeBiwEVrVoXWZmNkJLumUiYqekvwP+k+JWyKsiYl0r1tWhsuxuGiPXxTDXxTDXxbCW1EVLLqiamVl7+ReqZmYZcnI3M8uQk/sYSTpD0r2S1ktaWmH82ZJ+kl7fl3RiO+IcD7XqojTdiyTtSr+DyFI9dSGpT9KdktZJ+s54xzie6jhOZkj6qqQfp/p4czvibDVJV0naJumuKuMl6V9TPf1E0skNrzQi/Brli+Ii8S+A5wBPA34MHDdimj8BDkvDZwI/aHfc7aqL0nT/BXwdeG27427jfnEoxS+1n53eP6vdcbe5Pj4IfDwNHwE8Ajyt3bG3oC7+DDgZuKvK+LOAmyl+I/SSZuQLt9zHZs/jFSLid8DuxyvsERHfj4jt6e0ainv9c1SzLpJ3A18Cto1ncOOsnrr4W+CGiNgIEBGTvT4COESSgC6K5L5zfMNsvYhYTbFt1SwAPhuFNcChkmY1sk4n97GZAzxQer8plVVzLsW3co5q1oWkOcBrgCvGMa52qGe/eB5wmKQBSWslvWncoht/9dTHZcALKX7kOAi8NyJ+Pz7hdZTR5pSa/M86xqbm4xX2TCjNp0juL2tpRO1TT138M3B+ROwqGmjZqqcupgKnAKcB04HbJK2JiJ+1Org2qKc+TgfuBF4OPBe4RdJ3I+KxFsfWaerOKfVych+buh6vIOkPgc8AZ0bEw+MU23irpy56gf6U2GcCZ0naGRFfGZcIx089dbEJeCgingCekLQaOBHIMbnXUx9vBi6OouN5vaT7gRcAt49PiB2j6Y9scbfM2NR8vIKkZwM3AG/MtFW2W826iIijI6InInqA64F3ZZjYob7HbtwI/KmkqZKeDrwYuGec4xwv9dTHRoqzGCR1Uzwh9r5xjbIzrALelO6aeQmwIyIebGSBbrmPQVR5vIKkd6TxVwD/G3gmcHlqse6MDJ+CV2ddTAr11EVE3CPpG8BPgN9T/JeyirfHTXR17hsfBa6WNEjRNXF+RGT3KGBJ1wF9wExJm4ALgANhTz18neKOmfXAbyjOaBpbZ7oNx8zMMuJuGTOzDDm5m5llyMndzCxDTu5mZhlycjczy5CTu5lZhpzczcwy9P8B2UtF6rUqH9UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "content_df[content_df['user_id']>100]['answered_correctly'].hist(bins=100)\n",
    "plt.title(\"Distribution of correctness rate of questions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c89045c5",
   "metadata": {},
   "source": [
    "### Distribution of time use on previous questions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c91bc2cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['prior_question_elapsed_time'].compute().hist(bins=100)\n",
    "plt.title(\"Distribution of time spent on previous questions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bfd5174",
   "metadata": {},
   "source": [
    "### Is time elapsed on previous question related to correctness?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4cdbf6b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "prior_question_qcut = df['prior_question_elapsed_time'].map_partitions(pd.qcut, 10, labels=False,\\\n",
    "meta=df['prior_question_elapsed_time'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "576cf140",
   "metadata": {},
   "outputs": [],
   "source": [
    "pq_df = (df.groupby(prior_question_qcut).agg({'answered_correctly': 'mean'}).compute()\n",
    "           .reset_index().rename(columns={'prior_question_elapsed_time': 'prior_question_elapsed_time_decile'}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7938b09b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x='prior_question_elapsed_time_decile', y='answered_correctly', data=pq_df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2e51113",
   "metadata": {},
   "source": [
    "### Does explanation for prior question correlate to predict the correctness ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "df244a2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>answered_correctly</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prior_question_had_explanation</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>11152266</td>\n",
       "      <td>0.237025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>89685560</td>\n",
       "      <td>0.673189</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 user_id  answered_correctly\n",
       "prior_question_had_explanation                              \n",
       "False                           11152266            0.237025\n",
       "True                            89685560            0.673189"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby('prior_question_had_explanation').agg({'user_id': 'count', 'answered_correctly': 'mean'}).compute()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeedcb34",
   "metadata": {},
   "source": [
    "### Does the section of the test (variable part) correlate to predict answer correctness?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8ce59dec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>part</th>\n",
       "      <th>user_id</th>\n",
       "      <th>num_answered_correctly</th>\n",
       "      <th>prop_correct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>7454570</td>\n",
       "      <td>5553880</td>\n",
       "      <td>0.745030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>18743404</td>\n",
       "      <td>13283284</td>\n",
       "      <td>0.708691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>8639907</td>\n",
       "      <td>6060471</td>\n",
       "      <td>0.701451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>8067676</td>\n",
       "      <td>5090641</td>\n",
       "      <td>0.630992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>40908153</td>\n",
       "      <td>24957361</td>\n",
       "      <td>0.610083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>10501472</td>\n",
       "      <td>7029513</td>\n",
       "      <td>0.669384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>4956118</td>\n",
       "      <td>3269027</td>\n",
       "      <td>0.659594</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   part   user_id  num_answered_correctly  prop_correct\n",
       "0     1   7454570                 5553880      0.745030\n",
       "1     2  18743404                13283284      0.708691\n",
       "2     3   8639907                 6060471      0.701451\n",
       "3     4   8067676                 5090641      0.630992\n",
       "4     5  40908153                24957361      0.610083\n",
       "5     6  10501472                 7029513      0.669384\n",
       "6     7   4956118                 3269027      0.659594"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part_agg = content_df.groupby('part', as_index=False).agg({'user_id': 'sum', 'num_answered_correctly': 'sum'})\n",
    "part_agg['prop_correct'] = part_agg['num_answered_correctly'] / part_agg['user_id']\n",
    "part_agg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d8c01cea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x='part', y='prop_correct', data=part_agg, hue=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a67992a7",
   "metadata": {},
   "source": [
    "### Explore the tags"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2c16ff79",
   "metadata": {},
   "outputs": [],
   "source": [
    "#clean the tags, convert the string to list\n",
    "content_df['tags'].fillna('', inplace=True)\n",
    "content_df['tags_list'] = content_df['tags'].apply(lambda x: [int(t) for t in x.split()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "67680055",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tag</th>\n",
       "      <th>num_questions</th>\n",
       "      <th>num_answered_correctly</th>\n",
       "      <th>prop_correct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>326679</td>\n",
       "      <td>204655</td>\n",
       "      <td>0.626471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2409509</td>\n",
       "      <td>1465604</td>\n",
       "      <td>0.608258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1727202</td>\n",
       "      <td>1206066</td>\n",
       "      <td>0.698277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>290278</td>\n",
       "      <td>187107</td>\n",
       "      <td>0.644579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>499255</td>\n",
       "      <td>320362</td>\n",
       "      <td>0.641680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>183</td>\n",
       "      <td>190269</td>\n",
       "      <td>130334</td>\n",
       "      <td>0.684999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>184</td>\n",
       "      <td>288058</td>\n",
       "      <td>201479</td>\n",
       "      <td>0.699439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>185</td>\n",
       "      <td>192498</td>\n",
       "      <td>139308</td>\n",
       "      <td>0.723685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>186</td>\n",
       "      <td>9002</td>\n",
       "      <td>5055</td>\n",
       "      <td>0.561542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>187</td>\n",
       "      <td>252069</td>\n",
       "      <td>215776</td>\n",
       "      <td>0.856020</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>188 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     tag  num_questions  num_answered_correctly  prop_correct\n",
       "0      0         326679                  204655      0.626471\n",
       "1      1        2409509                 1465604      0.608258\n",
       "2      2        1727202                 1206066      0.698277\n",
       "3      3         290278                  187107      0.644579\n",
       "4      4         499255                  320362      0.641680\n",
       "..   ...            ...                     ...           ...\n",
       "183  183         190269                  130334      0.684999\n",
       "184  184         288058                  201479      0.699439\n",
       "185  185         192498                  139308      0.723685\n",
       "186  186           9002                    5055      0.561542\n",
       "187  187         252069                  215776      0.856020\n",
       "\n",
       "[188 rows x 4 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import chain\n",
    "\n",
    "tags_df = content_df.apply(lambda x: [(t, x['user_id'], x['num_answered_correctly']) for t in x['tags_list']],axis=1).values\n",
    "tags_df = chain.from_iterable(tags_df)\n",
    "tags_df = pd.DataFrame(tags_df, columns=['tag', 'num_questions', 'num_answered_correctly'])\n",
    "tags_df = tags_df.groupby('tag', as_index=False).sum()\n",
    "tags_df['prop_correct'] = tags_df['num_answered_correctly'] / tags_df['num_questions']\n",
    "tags_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "c3282944",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tags_df['prop_correct'].hist(bins=20)\n",
    "plt.title(\"Distribution of correctness by tag\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "846cfa38",
   "metadata": {},
   "source": [
    "### Analysis about the user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3496a37f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_questions_answered</th>\n",
       "      <th>answered_correctly</th>\n",
       "      <th>total_time_spent</th>\n",
       "      <th>total_time_spent_mins</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>user_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>46</td>\n",
       "      <td>0.695652</td>\n",
       "      <td>668090043</td>\n",
       "      <td>11134.834050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>30</td>\n",
       "      <td>0.233333</td>\n",
       "      <td>571323</td>\n",
       "      <td>9.522050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2746</th>\n",
       "      <td>19</td>\n",
       "      <td>0.578947</td>\n",
       "      <td>835457</td>\n",
       "      <td>13.924283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5382</th>\n",
       "      <td>125</td>\n",
       "      <td>0.672000</td>\n",
       "      <td>2101551456</td>\n",
       "      <td>35025.857600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8623</th>\n",
       "      <td>109</td>\n",
       "      <td>0.642202</td>\n",
       "      <td>862338736</td>\n",
       "      <td>14372.312267</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         num_questions_answered  answered_correctly  total_time_spent  \\\n",
       "user_id                                                                 \n",
       "115                          46            0.695652         668090043   \n",
       "124                          30            0.233333            571323   \n",
       "2746                         19            0.578947            835457   \n",
       "5382                        125            0.672000        2101551456   \n",
       "8623                        109            0.642202         862338736   \n",
       "\n",
       "         total_time_spent_mins  \n",
       "user_id                         \n",
       "115               11134.834050  \n",
       "124                   9.522050  \n",
       "2746                 13.924283  \n",
       "5382              35025.857600  \n",
       "8623              14372.312267  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user_df = (df.query(\"content_type_id==0\")\n",
    "           .groupby('user_id')\n",
    "           .agg({'user_answer': 'count', 'answered_correctly': 'mean', 'timestamp': 'max'})\n",
    "           .rename(columns={'user_answer': 'num_questions_answered', 'timestamp': 'total_time_spent'})).compute()\n",
    "user_df['total_time_spent_mins'] = user_df['total_time_spent'] / 60000.0\n",
    "user_df.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99efb1b1",
   "metadata": {},
   "source": [
    "### Distribution of number of questions answered by each user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "b81d36dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_df[user_df['num_questions_answered'] < 2000]['num_questions_answered'].hist(bins=100)\n",
    "plt.title(\"Distribution of number of questions answered by users\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da089400",
   "metadata": {},
   "source": [
    "### Distribution of total time spent\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "b726a738",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_df['total_time_spent_mins'].hist(bins=100)\n",
    "plt.title(\"Distribution of total time spent\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "698e8186",
   "metadata": {},
   "source": [
    "### Potential Outliers : users with millions of minutes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a7edafc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "outlier_user_ids = df[df['timestamp'] > 1e6 * 60000][['user_id']].drop_duplicates()\n",
    "outlier_user_df = outlier_user_ids.merge(df, how='inner', on='user_id').compute()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "28f926cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>row_id</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>content_id</th>\n",
       "      <th>content_type_id</th>\n",
       "      <th>task_container_id</th>\n",
       "      <th>user_answer</th>\n",
       "      <th>answered_correctly</th>\n",
       "      <th>prior_question_elapsed_time</th>\n",
       "      <th>prior_question_had_explanation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2726001</td>\n",
       "      <td>136260</td>\n",
       "      <td>0</td>\n",
       "      <td>7900</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2726001</td>\n",
       "      <td>136261</td>\n",
       "      <td>23598</td>\n",
       "      <td>7876</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>27000.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2726001</td>\n",
       "      <td>136262</td>\n",
       "      <td>50822</td>\n",
       "      <td>175</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2726001</td>\n",
       "      <td>136263</td>\n",
       "      <td>70505</td>\n",
       "      <td>1278</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>25000.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2726001</td>\n",
       "      <td>136264</td>\n",
       "      <td>150225</td>\n",
       "      <td>2065</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17000.0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9246</th>\n",
       "      <td>2147192453</td>\n",
       "      <td>101221106</td>\n",
       "      <td>60402896564</td>\n",
       "      <td>832</td>\n",
       "      <td>0</td>\n",
       "      <td>888</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>12000.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9247</th>\n",
       "      <td>2147192453</td>\n",
       "      <td>101221107</td>\n",
       "      <td>60402924679</td>\n",
       "      <td>564</td>\n",
       "      <td>0</td>\n",
       "      <td>889</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9248</th>\n",
       "      <td>2147192453</td>\n",
       "      <td>101221108</td>\n",
       "      <td>60402951816</td>\n",
       "      <td>1068</td>\n",
       "      <td>0</td>\n",
       "      <td>890</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>18000.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9249</th>\n",
       "      <td>2147192453</td>\n",
       "      <td>101221109</td>\n",
       "      <td>60402980491</td>\n",
       "      <td>1083</td>\n",
       "      <td>0</td>\n",
       "      <td>891</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>18000.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9250</th>\n",
       "      <td>2147192453</td>\n",
       "      <td>101221110</td>\n",
       "      <td>61068075367</td>\n",
       "      <td>1113</td>\n",
       "      <td>0</td>\n",
       "      <td>892</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15000.0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3521921 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         user_id     row_id    timestamp  content_id  content_type_id  \\\n",
       "0        2726001     136260            0        7900                0   \n",
       "1        2726001     136261        23598        7876                0   \n",
       "2        2726001     136262        50822         175                0   \n",
       "3        2726001     136263        70505        1278                0   \n",
       "4        2726001     136264       150225        2065                0   \n",
       "...          ...        ...          ...         ...              ...   \n",
       "9246  2147192453  101221106  60402896564         832                0   \n",
       "9247  2147192453  101221107  60402924679         564                0   \n",
       "9248  2147192453  101221108  60402951816        1068                0   \n",
       "9249  2147192453  101221109  60402980491        1083                0   \n",
       "9250  2147192453  101221110  61068075367        1113                0   \n",
       "\n",
       "      task_container_id  user_answer  answered_correctly  \\\n",
       "0                     0            1                   0   \n",
       "1                     1            0                   0   \n",
       "2                     2            1                   0   \n",
       "3                     3            3                   1   \n",
       "4                     4            0                   0   \n",
       "...                 ...          ...                 ...   \n",
       "9246                888            3                   1   \n",
       "9247                889            0                   1   \n",
       "9248                890            0                   1   \n",
       "9249                891            1                   1   \n",
       "9250                892            0                   0   \n",
       "\n",
       "      prior_question_elapsed_time prior_question_had_explanation  \n",
       "0                             NaN                            NaN  \n",
       "1                         27000.0                          False  \n",
       "2                         21000.0                          False  \n",
       "3                         25000.0                          False  \n",
       "4                         17000.0                          False  \n",
       "...                           ...                            ...  \n",
       "9246                      12000.0                           True  \n",
       "9247                      16000.0                           True  \n",
       "9248                      18000.0                           True  \n",
       "9249                      18000.0                           True  \n",
       "9250                      15000.0                           True  \n",
       "\n",
       "[3521921 rows x 10 columns]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outlier_user_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "40c66231",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "sample_user = outlier_user_df[outlier_user_df['user_id']==np.random.choice(outlier_user_df['user_id'].unique())].copy()\n",
    "sample_user['timestamp_mins'] = sample_user['timestamp'] / 60000\n",
    "sample_user['timestamp_hrs'] = sample_user['timestamp_mins'] / 60\n",
    "plt.plot(sample_user['timestamp_hrs'].values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "110647fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>row_id</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>content_id</th>\n",
       "      <th>content_type_id</th>\n",
       "      <th>task_container_id</th>\n",
       "      <th>user_answer</th>\n",
       "      <th>answered_correctly</th>\n",
       "      <th>prior_question_elapsed_time</th>\n",
       "      <th>prior_question_had_explanation</th>\n",
       "      <th>timestamp_mins</th>\n",
       "      <th>timestamp_hrs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20613</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579423</td>\n",
       "      <td>0</td>\n",
       "      <td>128</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20614</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579424</td>\n",
       "      <td>25112</td>\n",
       "      <td>7860</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>53000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>0.418533</td>\n",
       "      <td>0.006976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20615</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579425</td>\n",
       "      <td>44017</td>\n",
       "      <td>7922</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>22000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>0.733617</td>\n",
       "      <td>0.012227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20616</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579426</td>\n",
       "      <td>65506</td>\n",
       "      <td>156</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1.091767</td>\n",
       "      <td>0.018196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20617</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579427</td>\n",
       "      <td>87518</td>\n",
       "      <td>51</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>17000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1.458633</td>\n",
       "      <td>0.024311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20618</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579428</td>\n",
       "      <td>111211</td>\n",
       "      <td>50</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>1.853517</td>\n",
       "      <td>0.030892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20619</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579429</td>\n",
       "      <td>130695</td>\n",
       "      <td>7896</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>2.178250</td>\n",
       "      <td>0.036304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20620</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579430</td>\n",
       "      <td>152339</td>\n",
       "      <td>7863</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>17000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>2.538983</td>\n",
       "      <td>0.042316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20621</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579431</td>\n",
       "      <td>175366</td>\n",
       "      <td>152</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>2.922767</td>\n",
       "      <td>0.048713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20622</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579432</td>\n",
       "      <td>201885</td>\n",
       "      <td>104</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>3.364750</td>\n",
       "      <td>0.056079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20623</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579433</td>\n",
       "      <td>227752</td>\n",
       "      <td>108</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>23000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>3.795867</td>\n",
       "      <td>0.063264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20624</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579434</td>\n",
       "      <td>249191</td>\n",
       "      <td>7900</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>23000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.153183</td>\n",
       "      <td>0.069220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20625</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579435</td>\n",
       "      <td>272569</td>\n",
       "      <td>7901</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.542817</td>\n",
       "      <td>0.075714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20626</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579436</td>\n",
       "      <td>296111</td>\n",
       "      <td>7971</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.935183</td>\n",
       "      <td>0.082253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20627</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579437</td>\n",
       "      <td>319028</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>5.317133</td>\n",
       "      <td>0.088619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20628</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579438</td>\n",
       "      <td>345059</td>\n",
       "      <td>183</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>5.750983</td>\n",
       "      <td>0.095850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20629</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579439</td>\n",
       "      <td>366449</td>\n",
       "      <td>7926</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>6.107483</td>\n",
       "      <td>0.101791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20630</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579440</td>\n",
       "      <td>400585</td>\n",
       "      <td>7927</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>6.676417</td>\n",
       "      <td>0.111274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20631</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579441</td>\n",
       "      <td>425551</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>31000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>7.092517</td>\n",
       "      <td>0.118209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20632</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579442</td>\n",
       "      <td>468554</td>\n",
       "      <td>7984</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>22000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>7.809233</td>\n",
       "      <td>0.130154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20633</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579443</td>\n",
       "      <td>498860</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>40000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>8.314333</td>\n",
       "      <td>0.138572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20634</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579444</td>\n",
       "      <td>527796</td>\n",
       "      <td>185</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>28000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>8.796600</td>\n",
       "      <td>0.146610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20635</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579445</td>\n",
       "      <td>548695</td>\n",
       "      <td>55</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>27000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>9.144917</td>\n",
       "      <td>0.152415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20636</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579446</td>\n",
       "      <td>572817</td>\n",
       "      <td>7876</td>\n",
       "      <td>0</td>\n",
       "      <td>23</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>18000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>9.546950</td>\n",
       "      <td>0.159116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20637</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579447</td>\n",
       "      <td>597112</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>9.951867</td>\n",
       "      <td>0.165864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20638</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579448</td>\n",
       "      <td>618234</td>\n",
       "      <td>172</td>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>10.303900</td>\n",
       "      <td>0.171732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20639</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579449</td>\n",
       "      <td>643211</td>\n",
       "      <td>7898</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>19000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>10.720183</td>\n",
       "      <td>0.178670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20640</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579450</td>\n",
       "      <td>669440</td>\n",
       "      <td>175</td>\n",
       "      <td>0</td>\n",
       "      <td>27</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>11.157333</td>\n",
       "      <td>0.185956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20641</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579451</td>\n",
       "      <td>688441</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>11.474017</td>\n",
       "      <td>0.191234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20642</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579452</td>\n",
       "      <td>713766</td>\n",
       "      <td>7859</td>\n",
       "      <td>0</td>\n",
       "      <td>29</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>11.896100</td>\n",
       "      <td>0.198268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20643</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579453</td>\n",
       "      <td>328306027</td>\n",
       "      <td>1232</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>22000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>5471.767117</td>\n",
       "      <td>91.196119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20644</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579454</td>\n",
       "      <td>19182738833</td>\n",
       "      <td>1278</td>\n",
       "      <td>0</td>\n",
       "      <td>31</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>17000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319712.313883</td>\n",
       "      <td>5328.538565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20645</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579455</td>\n",
       "      <td>19182857759</td>\n",
       "      <td>2065</td>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319714.295983</td>\n",
       "      <td>5328.571600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20646</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579456</td>\n",
       "      <td>19182857759</td>\n",
       "      <td>2063</td>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319714.295983</td>\n",
       "      <td>5328.571600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20647</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579457</td>\n",
       "      <td>19182857759</td>\n",
       "      <td>2064</td>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>21000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319714.295983</td>\n",
       "      <td>5328.571600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20648</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579458</td>\n",
       "      <td>19182948033</td>\n",
       "      <td>3364</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>24333.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319715.800550</td>\n",
       "      <td>5328.596676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20649</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579459</td>\n",
       "      <td>19182948033</td>\n",
       "      <td>3365</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>24333.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319715.800550</td>\n",
       "      <td>5328.596676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20650</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579460</td>\n",
       "      <td>19182948033</td>\n",
       "      <td>3363</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>24333.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319715.800550</td>\n",
       "      <td>5328.596676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20651</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579461</td>\n",
       "      <td>19183034910</td>\n",
       "      <td>2947</td>\n",
       "      <td>0</td>\n",
       "      <td>34</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>29000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319717.248500</td>\n",
       "      <td>5328.620808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20652</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579462</td>\n",
       "      <td>19183034910</td>\n",
       "      <td>2946</td>\n",
       "      <td>0</td>\n",
       "      <td>34</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>29000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319717.248500</td>\n",
       "      <td>5328.620808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20653</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579463</td>\n",
       "      <td>19183034910</td>\n",
       "      <td>2948</td>\n",
       "      <td>0</td>\n",
       "      <td>34</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>29000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>319717.248500</td>\n",
       "      <td>5328.620808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20654</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579464</td>\n",
       "      <td>19242606228</td>\n",
       "      <td>2594</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320710.103800</td>\n",
       "      <td>5345.168397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20655</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579465</td>\n",
       "      <td>19242606228</td>\n",
       "      <td>2595</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320710.103800</td>\n",
       "      <td>5345.168397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20656</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579466</td>\n",
       "      <td>19242606228</td>\n",
       "      <td>2593</td>\n",
       "      <td>0</td>\n",
       "      <td>35</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320710.103800</td>\n",
       "      <td>5345.168397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20657</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579467</td>\n",
       "      <td>19242643615</td>\n",
       "      <td>4492</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>24333.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320710.726917</td>\n",
       "      <td>5345.178782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20658</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579468</td>\n",
       "      <td>19242674231</td>\n",
       "      <td>4120</td>\n",
       "      <td>0</td>\n",
       "      <td>37</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>33000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320711.237183</td>\n",
       "      <td>5345.187286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20659</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579469</td>\n",
       "      <td>19242691648</td>\n",
       "      <td>4696</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>25000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320711.527467</td>\n",
       "      <td>5345.192124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20660</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579470</td>\n",
       "      <td>19242699512</td>\n",
       "      <td>6116</td>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320711.658533</td>\n",
       "      <td>5345.194309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20661</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579471</td>\n",
       "      <td>19242724703</td>\n",
       "      <td>6173</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320712.078383</td>\n",
       "      <td>5345.201306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20662</th>\n",
       "      <td>1922901440</td>\n",
       "      <td>90579472</td>\n",
       "      <td>19242735736</td>\n",
       "      <td>6370</td>\n",
       "      <td>0</td>\n",
       "      <td>41</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>22000.0</td>\n",
       "      <td>False</td>\n",
       "      <td>320712.262267</td>\n",
       "      <td>5345.204371</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          user_id    row_id    timestamp  content_id  content_type_id  \\\n",
       "20613  1922901440  90579423            0         128                0   \n",
       "20614  1922901440  90579424        25112        7860                0   \n",
       "20615  1922901440  90579425        44017        7922                0   \n",
       "20616  1922901440  90579426        65506         156                0   \n",
       "20617  1922901440  90579427        87518          51                0   \n",
       "20618  1922901440  90579428       111211          50                0   \n",
       "20619  1922901440  90579429       130695        7896                0   \n",
       "20620  1922901440  90579430       152339        7863                0   \n",
       "20621  1922901440  90579431       175366         152                0   \n",
       "20622  1922901440  90579432       201885         104                0   \n",
       "20623  1922901440  90579433       227752         108                0   \n",
       "20624  1922901440  90579434       249191        7900                0   \n",
       "20625  1922901440  90579435       272569        7901                0   \n",
       "20626  1922901440  90579436       296111        7971                0   \n",
       "20627  1922901440  90579437       319028          25                0   \n",
       "20628  1922901440  90579438       345059         183                0   \n",
       "20629  1922901440  90579439       366449        7926                0   \n",
       "20630  1922901440  90579440       400585        7927                0   \n",
       "20631  1922901440  90579441       425551           4                0   \n",
       "20632  1922901440  90579442       468554        7984                0   \n",
       "20633  1922901440  90579443       498860          45                0   \n",
       "20634  1922901440  90579444       527796         185                0   \n",
       "20635  1922901440  90579445       548695          55                0   \n",
       "20636  1922901440  90579446       572817        7876                0   \n",
       "20637  1922901440  90579447       597112           6                0   \n",
       "20638  1922901440  90579448       618234         172                0   \n",
       "20639  1922901440  90579449       643211        7898                0   \n",
       "20640  1922901440  90579450       669440         175                0   \n",
       "20641  1922901440  90579451       688441         100                0   \n",
       "20642  1922901440  90579452       713766        7859                0   \n",
       "20643  1922901440  90579453    328306027        1232                0   \n",
       "20644  1922901440  90579454  19182738833        1278                0   \n",
       "20645  1922901440  90579455  19182857759        2065                0   \n",
       "20646  1922901440  90579456  19182857759        2063                0   \n",
       "20647  1922901440  90579457  19182857759        2064                0   \n",
       "20648  1922901440  90579458  19182948033        3364                0   \n",
       "20649  1922901440  90579459  19182948033        3365                0   \n",
       "20650  1922901440  90579460  19182948033        3363                0   \n",
       "20651  1922901440  90579461  19183034910        2947                0   \n",
       "20652  1922901440  90579462  19183034910        2946                0   \n",
       "20653  1922901440  90579463  19183034910        2948                0   \n",
       "20654  1922901440  90579464  19242606228        2594                0   \n",
       "20655  1922901440  90579465  19242606228        2595                0   \n",
       "20656  1922901440  90579466  19242606228        2593                0   \n",
       "20657  1922901440  90579467  19242643615        4492                0   \n",
       "20658  1922901440  90579468  19242674231        4120                0   \n",
       "20659  1922901440  90579469  19242691648        4696                0   \n",
       "20660  1922901440  90579470  19242699512        6116                0   \n",
       "20661  1922901440  90579471  19242724703        6173                0   \n",
       "20662  1922901440  90579472  19242735736        6370                0   \n",
       "\n",
       "       task_container_id  user_answer  answered_correctly  \\\n",
       "20613                  0            0                   1   \n",
       "20614                  1            0                   1   \n",
       "20615                  2            1                   1   \n",
       "20616                  3            2                   1   \n",
       "20617                  4            0                   1   \n",
       "20618                  5            3                   1   \n",
       "20619                  6            2                   1   \n",
       "20620                  7            0                   1   \n",
       "20621                  8            1                   1   \n",
       "20622                  9            2                   1   \n",
       "20623                 10            3                   1   \n",
       "20624                 11            0                   1   \n",
       "20625                 12            1                   1   \n",
       "20626                 13            2                   1   \n",
       "20627                 14            1                   1   \n",
       "20628                 15            1                   1   \n",
       "20629                 16            1                   1   \n",
       "20630                 17            3                   1   \n",
       "20631                 18            3                   1   \n",
       "20632                 19            0                   1   \n",
       "20633                 20            2                   0   \n",
       "20634                 21            3                   0   \n",
       "20635                 22            3                   1   \n",
       "20636                 23            3                   1   \n",
       "20637                 24            2                   1   \n",
       "20638                 25            1                   1   \n",
       "20639                 26            1                   0   \n",
       "20640                 27            2                   1   \n",
       "20641                 28            0                   1   \n",
       "20642                 29            2                   0   \n",
       "20643                 30            1                   1   \n",
       "20644                 31            3                   1   \n",
       "20645                 32            2                   1   \n",
       "20646                 32            2                   0   \n",
       "20647                 32            1                   1   \n",
       "20648                 33            1                   1   \n",
       "20649                 33            0                   0   \n",
       "20650                 33            1                   0   \n",
       "20651                 34            0                   0   \n",
       "20652                 34            2                   0   \n",
       "20653                 34            3                   0   \n",
       "20654                 35            0                   0   \n",
       "20655                 35            0                   1   \n",
       "20656                 35            3                   1   \n",
       "20657                 36            2                   1   \n",
       "20658                 37            3                   0   \n",
       "20659                 38            0                   1   \n",
       "20660                 39            3                   1   \n",
       "20661                 40            2                   1   \n",
       "20662                 41            2                   1   \n",
       "\n",
       "       prior_question_elapsed_time prior_question_had_explanation  \\\n",
       "20613                          NaN                            NaN   \n",
       "20614                      53000.0                          False   \n",
       "20615                      22000.0                          False   \n",
       "20616                      16000.0                          False   \n",
       "20617                      17000.0                          False   \n",
       "20618                      19000.0                          False   \n",
       "20619                      21000.0                          False   \n",
       "20620                      17000.0                          False   \n",
       "20621                      19000.0                          False   \n",
       "20622                      20000.0                          False   \n",
       "20623                      23000.0                          False   \n",
       "20624                      23000.0                          False   \n",
       "20625                      19000.0                          False   \n",
       "20626                      21000.0                          False   \n",
       "20627                      21000.0                          False   \n",
       "20628                      20000.0                          False   \n",
       "20629                      24000.0                          False   \n",
       "20630                      19000.0                          False   \n",
       "20631                      31000.0                          False   \n",
       "20632                      22000.0                          False   \n",
       "20633                      40000.0                          False   \n",
       "20634                      28000.0                          False   \n",
       "20635                      27000.0                          False   \n",
       "20636                      18000.0                          False   \n",
       "20637                      21000.0                          False   \n",
       "20638                      21000.0                          False   \n",
       "20639                      19000.0                          False   \n",
       "20640                      21000.0                          False   \n",
       "20641                      24000.0                          False   \n",
       "20642                      16000.0                          False   \n",
       "20643                      22000.0                          False   \n",
       "20644                      17000.0                          False   \n",
       "20645                      21000.0                          False   \n",
       "20646                      21000.0                          False   \n",
       "20647                      21000.0                          False   \n",
       "20648                      24333.0                          False   \n",
       "20649                      24333.0                          False   \n",
       "20650                      24333.0                          False   \n",
       "20651                      29000.0                          False   \n",
       "20652                      29000.0                          False   \n",
       "20653                      29000.0                          False   \n",
       "20654                      24000.0                          False   \n",
       "20655                      24000.0                          False   \n",
       "20656                      24000.0                          False   \n",
       "20657                      24333.0                          False   \n",
       "20658                      33000.0                          False   \n",
       "20659                      25000.0                          False   \n",
       "20660                      13000.0                          False   \n",
       "20661                       4000.0                          False   \n",
       "20662                      22000.0                          False   \n",
       "\n",
       "       timestamp_mins  timestamp_hrs  \n",
       "20613        0.000000       0.000000  \n",
       "20614        0.418533       0.006976  \n",
       "20615        0.733617       0.012227  \n",
       "20616        1.091767       0.018196  \n",
       "20617        1.458633       0.024311  \n",
       "20618        1.853517       0.030892  \n",
       "20619        2.178250       0.036304  \n",
       "20620        2.538983       0.042316  \n",
       "20621        2.922767       0.048713  \n",
       "20622        3.364750       0.056079  \n",
       "20623        3.795867       0.063264  \n",
       "20624        4.153183       0.069220  \n",
       "20625        4.542817       0.075714  \n",
       "20626        4.935183       0.082253  \n",
       "20627        5.317133       0.088619  \n",
       "20628        5.750983       0.095850  \n",
       "20629        6.107483       0.101791  \n",
       "20630        6.676417       0.111274  \n",
       "20631        7.092517       0.118209  \n",
       "20632        7.809233       0.130154  \n",
       "20633        8.314333       0.138572  \n",
       "20634        8.796600       0.146610  \n",
       "20635        9.144917       0.152415  \n",
       "20636        9.546950       0.159116  \n",
       "20637        9.951867       0.165864  \n",
       "20638       10.303900       0.171732  \n",
       "20639       10.720183       0.178670  \n",
       "20640       11.157333       0.185956  \n",
       "20641       11.474017       0.191234  \n",
       "20642       11.896100       0.198268  \n",
       "20643     5471.767117      91.196119  \n",
       "20644   319712.313883    5328.538565  \n",
       "20645   319714.295983    5328.571600  \n",
       "20646   319714.295983    5328.571600  \n",
       "20647   319714.295983    5328.571600  \n",
       "20648   319715.800550    5328.596676  \n",
       "20649   319715.800550    5328.596676  \n",
       "20650   319715.800550    5328.596676  \n",
       "20651   319717.248500    5328.620808  \n",
       "20652   319717.248500    5328.620808  \n",
       "20653   319717.248500    5328.620808  \n",
       "20654   320710.103800    5345.168397  \n",
       "20655   320710.103800    5345.168397  \n",
       "20656   320710.103800    5345.168397  \n",
       "20657   320710.726917    5345.178782  \n",
       "20658   320711.237183    5345.187286  \n",
       "20659   320711.527467    5345.192124  \n",
       "20660   320711.658533    5345.194309  \n",
       "20661   320712.078383    5345.201306  \n",
       "20662   320712.262267    5345.204371  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_user.head(50)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d08ca0c2",
   "metadata": {},
   "source": [
    "### Distribution of user ablility, some people always have higher correct rate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "4fc90b25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_df[user_df['num_questions_answered']>10]['answered_correctly'].hist(bins=50)\n",
    "plt.title(\"Distribution of answer correctness by users\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6670005f",
   "metadata": {},
   "source": [
    "### Distribution of lectures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "ce97f2fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 418 entries, 0 to 417\n",
      "Data columns (total 4 columns):\n",
      " #   Column      Non-Null Count  Dtype \n",
      "---  ------      --------------  ----- \n",
      " 0   lecture_id  418 non-null    int64 \n",
      " 1   tag         418 non-null    int64 \n",
      " 2   part        418 non-null    int64 \n",
      " 3   type_of     418 non-null    object\n",
      "dtypes: int64(3), object(1)\n",
      "memory usage: 13.2+ KB\n"
     ]
    }
   ],
   "source": [
    "lectures_df = pd.read_csv('lectures.csv')\n",
    "lectures_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "98da0791",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lecture_id</th>\n",
       "      <th>tag</th>\n",
       "      <th>part</th>\n",
       "      <th>type_of</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>89</td>\n",
       "      <td>159</td>\n",
       "      <td>5</td>\n",
       "      <td>concept</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>concept</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185</td>\n",
       "      <td>45</td>\n",
       "      <td>6</td>\n",
       "      <td>concept</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>192</td>\n",
       "      <td>79</td>\n",
       "      <td>5</td>\n",
       "      <td>solving question</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>317</td>\n",
       "      <td>156</td>\n",
       "      <td>5</td>\n",
       "      <td>solving question</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   lecture_id  tag  part           type_of\n",
       "0          89  159     5           concept\n",
       "1         100   70     1           concept\n",
       "2         185   45     6           concept\n",
       "3         192   79     5  solving question\n",
       "4         317  156     5  solving question"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lectures_df.head()\n"
   ]
  }
 ],
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