NOTES_Intro_to_Data_Analysis-1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'account_key': u'448',\n",
       " u'cancel_date': u'2015-01-14',\n",
       " u'days_to_cancel': u'65',\n",
       " u'is_canceled': u'True',\n",
       " u'is_udacity': u'True',\n",
       " u'join_date': u'2014-11-10',\n",
       " u'status': u'canceled'}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import unicodecsv\n",
    "\n",
    "enrollments = []\n",
    "f = open('enrollments.csv', 'rb')   # read file in binary mode\n",
    "reader = unicodecsv.DictReader(f)   # Read csv as dictonary\n",
    "\n",
    "for row in reader:\n",
    "    enrollments.append(row)\n",
    "    \n",
    "f.close()\n",
    "\n",
    "enrollments[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'account_key': u'448',\n",
       " u'cancel_date': u'2015-01-14',\n",
       " u'days_to_cancel': u'65',\n",
       " u'is_canceled': u'True',\n",
       " u'is_udacity': u'True',\n",
       " u'join_date': u'2014-11-10',\n",
       " u'status': u'canceled'}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Better way of writing the code code\n",
    "import unicodecsv\n",
    "\n",
    "with open('enrollments.csv', 'rb') as f:\n",
    "    enrollments = list(unicodecsv.DictReader(f))\n",
    "    \n",
    "enrollments[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with open('daily_engagement.csv', 'rb') as f:\n",
    "    daily_engagement = list(unicodecsv.DictReader(f))\n",
    "    \n",
    "with open('project_submissions.csv', 'rb') as f:\n",
    "    project_submissions = list(unicodecsv.DictReader(f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixing data types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'account_key': u'448',\n",
       " u'cancel_date': datetime.datetime(2015, 1, 14, 0, 0),\n",
       " u'days_to_cancel': 65,\n",
       " u'is_canceled': True,\n",
       " u'is_udacity': True,\n",
       " u'join_date': datetime.datetime(2014, 11, 10, 0, 0),\n",
       " u'status': u'canceled'}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from datetime import datetime as dt\n",
    "\n",
    "# Takes a date as a string, and returns a Python datetime object. \n",
    "# If there is no date given, returns None\n",
    "def parse_date(date):\n",
    "    if date == '':\n",
    "        return None\n",
    "    else:\n",
    "        return dt.strptime(date, '%Y-%m-%d')\n",
    "    \n",
    "# Takes a string which is either an empty string or represents an integer,\n",
    "# and returns an int or None.\n",
    "def parse_maybe_int(i):\n",
    "    if i == '':\n",
    "        return None\n",
    "    else:\n",
    "        return int(i)\n",
    "\n",
    "# Clean up the data types in the enrollments table\n",
    "for enrollment in enrollments:\n",
    "    enrollment['cancel_date'] = parse_date(enrollment['cancel_date'])\n",
    "    enrollment['days_to_cancel'] = parse_maybe_int(enrollment['days_to_cancel'])\n",
    "    enrollment['is_canceled'] = enrollment['is_canceled'] == 'True'\n",
    "    enrollment['is_udacity'] = enrollment['is_udacity'] == 'True'\n",
    "    enrollment['join_date'] = parse_date(enrollment['join_date'])\n",
    "    \n",
    "enrollments[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'acct': u'0',\n",
       " u'lessons_completed': 0,\n",
       " u'num_courses_visited': 1,\n",
       " u'projects_completed': 0,\n",
       " u'total_minutes_visited': 11.6793745,\n",
       " u'utc_date': datetime.datetime(2015, 1, 9, 0, 0)}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Clean up the data types in the daily_engagement table\n",
    "for engagement in daily_engagement:\n",
    "    engagement['lessons_completed'] = int(float(engagement['lessons_completed']))\n",
    "    engagement['num_courses_visited'] = int(float(engagement['num_courses_visited']))\n",
    "    engagement['projects_completed'] = int(float(engagement['projects_completed']))\n",
    "    engagement['total_minutes_visited'] = float(engagement['total_minutes_visited'])\n",
    "    engagement['utc_date'] = parse_date(engagement['utc_date'])\n",
    "    \n",
    "daily_engagement[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'account_key': u'256',\n",
       " u'assigned_rating': u'UNGRADED',\n",
       " u'completion_date': datetime.datetime(2015, 1, 16, 0, 0),\n",
       " u'creation_date': datetime.datetime(2015, 1, 14, 0, 0),\n",
       " u'lesson_key': u'3176718735',\n",
       " u'processing_state': u'EVALUATED'}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Clean up the data types in the project_submissions table\n",
    "for submission in project_submissions:\n",
    "    submission['completion_date'] = parse_date(submission['completion_date'])\n",
    "    submission['creation_date'] = parse_date(submission['creation_date'])\n",
    "\n",
    "project_submissions[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do students who pass the project are different from students who fail ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "### For each of these three tables, find the number of rows in the table and\n",
    "### the number of unique students in the table. To find the number of unique\n",
    "### students, you might want to create a set of the account keys in each table.\n",
    "\n",
    "def get_uniq_num_by_key(dict_list, key):\n",
    "    uniq_set = set()\n",
    "    for e in dict_list:\n",
    "        uniq_set.add(e[key])\n",
    "    return len(uniq_set)\n",
    "\n",
    "enrollment_num_rows = len(enrollments)    \n",
    "enrollment_num_unique_students = get_uniq_num_by_key(enrollments, 'account_key')\n",
    "\n",
    "engagement_num_rows = len(daily_engagement)\n",
    "engagement_num_unique_students = get_uniq_num_by_key(daily_engagement, 'acct')\n",
    "\n",
    "submission_num_rows = len(project_submissions)\n",
    "submission_num_unique_students = get_uniq_num_by_key(project_submissions, 'account_key')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1640 1302\n"
     ]
    }
   ],
   "source": [
    "print enrollment_num_rows, enrollment_num_unique_students"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "136240 1237\n"
     ]
    }
   ],
   "source": [
    "print engagement_num_rows, engagement_num_unique_students"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3642 743\n"
     ]
    }
   ],
   "source": [
    "print submission_num_rows, submission_num_unique_students"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From `daily_engagement` dict, its better to rename the key `acct` to `account_key` for uniformity across sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for d in daily_engagement:\n",
    "    d['account_key'] = d['acct']\n",
    "    del d['acct']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'account_key': u'0',\n",
       " u'lessons_completed': 0,\n",
       " u'num_courses_visited': 1,\n",
       " u'projects_completed': 0,\n",
       " u'total_minutes_visited': 11.6793745,\n",
       " u'utc_date': datetime.datetime(2015, 1, 9, 0, 0)}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily_engagement[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, num of students enrolled is less than the students who are daily engaged. Why is this so ?  \n",
    "Lets find one such student. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "set([u'1304', u'1129', u'1186', u'875', u'1222', u'1213', u'1120', u'749', u'1148', u'707', u'766', u'1125', u'1237', u'870', u'878', u'819', u'1191', u'1190', u'1145', u'733', u'799', u'871', u'1270', u'654', u'727', u'737', u'739', u'914', u'1219', u'1291', u'1010', u'889', u'817', u'1025', u'997', u'996', u'981', u'1171', u'717', u'1218', u'1273', u'1238', u'902', u'711', u'750', u'664', u'1069', u'1284', u'841', u'1044', u'1086', u'1155', u'1079', u'968', u'789', u'1241', u'964', u'725', u'884', u'728', u'1101', u'803', u'802', u'1063', u'926'])\n"
     ]
    }
   ],
   "source": [
    "def get_unique_accounts(data_list):\n",
    "    uniq_set = set()\n",
    "    for e in data_list:\n",
    "        uniq_set.add(e['account_key'])\n",
    "    return uniq_set\n",
    "\n",
    "enrollments_uniq_acct = get_unique_accounts(enrollments)\n",
    "daily_engagement_uniq_acct = get_unique_accounts(daily_engagement)\n",
    "\n",
    "print(enrollments_uniq_acct - daily_engagement_uniq_acct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{u'status': u'canceled', u'is_udacity': False, u'is_canceled': True, u'join_date': datetime.datetime(2015, 3, 7, 0, 0), u'account_key': u'1129', u'cancel_date': datetime.datetime(2015, 3, 7, 0, 0), u'days_to_cancel': 0}\n"
     ]
    }
   ],
   "source": [
    "for student in enrollments:\n",
    "    if student['account_key'] == '1129':  # take account 1129 for example\n",
    "        print student\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This account has the same `join_date` and `cancel_date`. Such students did not participate in the enrollments.  \n",
    "We also know the student with `is_udacity` `True` are udacity test accounts.  \n",
    "Remove these 2 cases to clean the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "udacity_test_accounts = set()\n",
    "for student in enrollments:\n",
    "    if student['is_udacity']:\n",
    "        udacity_test_accounts.add(student['account_key'])\n",
    "\n",
    "print len(udacity_test_accounts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are **6** Udacity test accounts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def remove_udacity_accounts(data_list):\n",
    "    non_udacity_data = []\n",
    "    for e in data_list:\n",
    "        if e['account_key'] not in udacity_test_accounts:\n",
    "            non_udacity_data.append(e)\n",
    "    return non_udacity_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1622\n",
      "135656\n",
      "3634\n"
     ]
    }
   ],
   "source": [
    "non_udacity_enrollments = remove_udacity_accounts(enrollments)\n",
    "non_udacity_engagements = remove_udacity_accounts(daily_engagement)\n",
    "non_udacity_submissions = remove_udacity_accounts(project_submissions)\n",
    "\n",
    "print len(non_udacity_enrollments)\n",
    "print len(non_udacity_engagements)\n",
    "print len(non_udacity_submissions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "995"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paid_students = {}\n",
    "for student in non_udacity_enrollments:\n",
    "    if not student['is_canceled'] or student['days_to_cancel'] > 7:\n",
    "        account_key = student['account_key']\n",
    "        enrollment_date = student['join_date']\n",
    "        paid_students[account_key] = enrollment_date\n",
    "        \n",
    "len(paid_students)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def within_one_week(join_date, engagement_date):\n",
    "    time_delta = engagement_date - join_date\n",
    "    return time_delta.days < 7 and time_delta.days >= 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def remove_free_trial_cancels(data):\n",
    "    new_data = []\n",
    "    for data_point in data:\n",
    "        if data_point['account_key'] in paid_students:\n",
    "            new_data.append(data_point)\n",
    "    \n",
    "    return new_data\n",
    "\n",
    "paid_engagements = remove_free_trial_cancels(non_udacity_engagements)\n",
    "paid_enrollments = remove_free_trial_cancels(non_udacity_enrollments)\n",
    "paid_submissions = remove_free_trial_cancels(non_udacity_submissions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for engagement in paid_engagements:\n",
    "    if engagement['num_courses_visited'] > 0:\n",
    "        engagement['has_visited'] = 1\n",
    "    else:\n",
    "        engagement['has_visited'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6920\n"
     ]
    }
   ],
   "source": [
    "## Create a list of rows from the engagement table including only rows where\n",
    "## the student is one of the paid students you just found, and the date is within\n",
    "## one week of the student's join date.\n",
    "\n",
    "paid_engagement_in_first_week = []\n",
    "\n",
    "for engagement in paid_engagements:\n",
    "    engagement_date = engagement['utc_date']\n",
    "    join_date = paid_students[engagement['account_key']]\n",
    "    \n",
    "    if within_one_week(join_date, engagement_date):\n",
    "        paid_engagement_in_first_week.append(engagement)\n",
    "        \n",
    "print len(paid_engagement_in_first_week)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring Student Engagement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "# Create a dictionary of engagement grouped by student.\n",
    "# The keys are account keys, and the values are lists of engagement records.\n",
    "\n",
    "def group_data(data, key_name):\n",
    "    grouped_data = defaultdict(list)\n",
    "    for data_point in data:\n",
    "        key = data_point[key_name]\n",
    "        grouped_data[key].append(data_point)\n",
    "    return grouped_data\n",
    "\n",
    "engagement_by_account = group_data(paid_engagement_in_first_week, 'account_key')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a dictionary with the total minutes each student spent in the classroom during the first week.\n",
    "# The keys are account keys, and the values are numbers (total minutes)\n",
    "\n",
    "def sum_grouped_items(grouped_data, field_name):\n",
    "    summed_data = {}\n",
    "    for key, data_points in grouped_data.items():\n",
    "        total = 0\n",
    "        for data_point in data_points:\n",
    "            total += data_point[field_name]\n",
    "        summed_data[key] = total\n",
    "    return summed_data\n",
    "        \n",
    "total_minutes_by_account = sum_grouped_items(engagement_by_account, 'total_minutes_visited')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**To apply statistical operations such as calculating mean of a distribution, we use `numpy` library.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 305.414718908\n",
      "Stadard deviation: 405.91261032\n",
      "Mininum: 0.0\n",
      "Maximum: 3564.7332645\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7f47d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# Summarize the data about minutes spent in the classroom\n",
    "def describe_data(data):\n",
    "    print 'Mean:', np.mean(data)\n",
    "    print 'Stadard deviation:', np.std(data)\n",
    "    print 'Mininum:', np.min(data)\n",
    "    print 'Maximum:', np.max(data)\n",
    "    plt.hist(data)\n",
    "    \n",
    "describe_data(total_minutes_by_account.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summarize data based on lessons completed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Summarize data based on lessons completed\n",
    "lessons_completed_by_account = sum_grouped_items(engagement_by_account, 'lessons_completed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 146.888888889\n",
      "Stadard deviation: 196.647142785\n",
      "Mininum: 0\n",
      "Maximum: 625\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAEACAYAAABF+UbAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7edb350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "describe_data(lessons_completed_by_account.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Find the distribution of number of days a student has visited the classroom in their first week**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 246.555555556\n",
      "Stadard deviation: 428.414936743\n",
      "Mininum: 1\n",
      "Maximum: 1333\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEACAYAAACj0I2EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7d3bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "days_visited_by_account = sum_grouped_items(engagement_by_account, 'has_visited')\n",
    "describe_data(days_visited_by_account.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculate the students who passed the subway project and not passed the passed the project**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "647"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# keys for subway project\n",
    "subway_project_lesson_keys = ['746169184', '3176718735']\n",
    "pass_subway_project = set()\n",
    "\n",
    "for submission in paid_submissions:\n",
    "    project = submission['lesson_key']\n",
    "    rating = submission['assigned_rating']\n",
    "    \n",
    "    if project in subway_project_lesson_keys and rating in ['PASSED', 'DISTINCTION']:\n",
    "        pass_subway_project.add(submission['account_key'])\n",
    "        \n",
    "len(pass_subway_project)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4528\n",
      "2392\n"
     ]
    }
   ],
   "source": [
    "passing_engagement = []\n",
    "non_passing_engagement = []\n",
    "\n",
    "for engagement in paid_engagement_in_first_week:\n",
    "    if engagement['account_key'] in pass_subway_project:\n",
    "        passing_engagement.append(engagement)\n",
    "    else:\n",
    "        non_passing_engagement.append(engagement)\n",
    "        \n",
    "print len(passing_engagement)\n",
    "print len(non_passing_engagement)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'account_key': u'0',\n",
       " 'has_visited': 1,\n",
       " u'lessons_completed': 0,\n",
       " u'num_courses_visited': 1,\n",
       " u'projects_completed': 0,\n",
       " u'total_minutes_visited': 11.6793745,\n",
       " u'utc_date': datetime.datetime(2015, 1, 9, 0, 0)}"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "passing_engagement[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_eng_by_account = group_data(passing_engagement, 'account_key')\n",
    "np_eng_by_account = group_data(non_passing_engagement, 'account_key')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passing students\n",
      "Mean: 391.481722325\n",
      "Stadard deviation: 439.653061726\n",
      "Mininum: 0.0\n",
      "Maximum: 3564.7332645\n",
      "--------------------------------------------------------------------------------\n",
      "Non passing students\n",
      "Mean: 145.399341866\n",
      "Stadard deviation: 268.97150373\n",
      "Mininum: 0.0\n",
      "Maximum: 1768.52274933\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNire4W5GAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7cc7b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print 'Passing students'\n",
    "p_eng_minutes = sum_grouped_items(p_eng_by_account, 'total_minutes_visited')\n",
    "p_eng_minutes_val = p_eng_minutes.values()\n",
    "describe_data(p_eng_minutes_val)\n",
    "\n",
    "print '-'*80\n",
    "print 'Non passing students'\n",
    "np_eng_minutes = sum_grouped_items(np_eng_by_account, 'total_minutes_visited')\n",
    "np_eng_minutes_val = np_eng_minutes.values()\n",
    "describe_data(np_eng_minutes_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passing students\n",
      "Mean: 2.04327666151\n",
      "Stadard deviation: 3.1428602763\n",
      "Mininum: 0\n",
      "Maximum: 36\n",
      "--------------------------------------------------------------------------------\n",
      "Non passing students\n",
      "Mean: 0.867816091954\n",
      "Stadard deviation: 2.54833703959\n",
      "Mininum: 0\n",
      "Maximum: 27\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7af6490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print 'Passing students'\n",
    "p_eng_lessons_completed = sum_grouped_items(p_eng_by_account, 'lessons_completed')\n",
    "p_eng_lessons_completed_val = p_eng_lessons_completed.values()\n",
    "describe_data(p_eng_lessons_completed_val)\n",
    "\n",
    "print '-'*80\n",
    "print 'Non passing students'\n",
    "np_eng_lessons_completed = sum_grouped_items(np_eng_by_account, 'lessons_completed')\n",
    "np_eng_lessons_completed_val = np_eng_lessons_completed.values()\n",
    "describe_data(np_eng_lessons_completed_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passing students\n",
      "Mean: 3.42967542504\n",
      "Stadard deviation: 2.21298340866\n",
      "Mininum: 0\n",
      "Maximum: 7\n",
      "--------------------------------------------------------------------------------\n",
      "Non passing students\n",
      "Mean: 1.95114942529\n",
      "Stadard deviation: 1.88929952676\n",
      "Mininum: 0\n",
      "Maximum: 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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wPvDZrtYngJ39lrSwJE8DtgM39F3LfJI8H/gQsBX4LeCZSd650Pp9hPsjwPPmzG/plmmF\nul20G4EvVdVNfddzKt1u+deAV/ZdyzwuALZ349nXAW9IMu94Zt+q6gfd9x8CX2V2uHPcPAwcqapv\nd/M3Mhv24+qtwB3dNh1HrwRur6rHquo48PfAaxdauY9w/xbwgiRbuyO97wDG9ayEce+9PekLwMGq\n+kzfhcwnyW8k2dRNnwG8Ebi736pOVlUfq6rnVdXzmf27PFBVf9x3XSdKcma3p0aSs4A3Af/ab1Un\nq6oZ4EiSF3aLLgTGdTgO4FLGdEimcwh4TZJnJAmz23PB64dGfm+ZtXKBU5IvA1PAc5I8BFzx5IGh\ncZLkAuBdwH3dmHYBH6uqf+y3sv/nN4G93R/kaczuYfxzzzWtZRPAV7tbeGwErq2qfT3XtJDLgWu7\nIY/vA+/tuZ55JTmT2YOpf9J3LQupqnu6Pck7gOPAXcA1C63vRUyS1CAPqEpSgwx3SWqQ4S5JDTLc\nJalBhrskNchwl6QGGe6S1CDDXZIa9L9S+Kvq9FGYjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7a8aad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print 'Passing students'\n",
    "p_eng_has_visited = sum_grouped_items(p_eng_by_account, 'has_visited')\n",
    "p_eng_has_visited_val = p_eng_has_visited.values()\n",
    "describe_data(p_eng_has_visited_val)\n",
    "\n",
    "print '-'*80\n",
    "print 'Non passing students'\n",
    "np_eng_has_visited = sum_grouped_items(np_eng_by_account, 'has_visited')\n",
    "np_eng_has_visited_val = np_eng_has_visited.values()\n",
    "describe_data(np_eng_has_visited_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Findings**: \n",
    "\n",
    "Clearly, passing students spend more time in the classroom. 6.5 hrs and 2.5 hrs is striking amount of difference.  \n",
    "Also, there are bright students who spend less time but are able to pass.  \n",
    "But HARD WORK ALWAYS PAYS OFF - Weak students who work hard (3500+ minutes spent in classroom) are also able to pass."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Making historgrams in Python** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  0.,  1.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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b7P13gReq6pvrvL7o+3/e+Rd5/5N8NMmuwfGHgM+z+hcnhi3s/k8y/6Luf1XdVVX7qupP\nWW3mk1V168iyqfa+83+7pia4eQq4KckdwHvAu8DNXc8xrSQ/AHrAR5K8BtwDXMQ2ufFr3Pws9t4f\nBG4BTg6uqxZwF6t/U2vh93+S+Vng/Qc+Bnw/SVj9b/fhqvpJts+Nj2PnZ7H3/xxd7L03Q0lSw/y/\n/5Okhhl5SWqYkZekhhl5SWqYkZekhhl5SWqYkZekhhl5SWrY/wNxoPZT1tGF8gAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb79d34d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = [1, 2, 1, 3, 3, 1, 4, 2]\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line `%matplotlib inline` is specifically for IPython notebook, and causes your plots to appear in your notebook rather than a new window. If you are not using IPython notebook, you should not include this line, and instead you should add the line `plt.show()` at the bottom to show the plot in a new window."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Findings after drawing the histograms:**  \n",
    "\n",
    "Passing students visit the classroom more. Num of students who visited the classroom once or twice equals the num of students who visit the six or seven times."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation does not imply Causation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Correlation**: Students who pass the first project are more likely to visit the classroom in the first week.  \n",
    "**Causation**: Does visiting the classroom multiple times **cause** the students to pass the project ? *That is not necessary.*  \n",
    "\n",
    "To determine this we need to conduct some experiments. These experiments in statistical jargon are called **A/B Testing**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Making predictions**  \n",
    "\n",
    "Which students are likely to pass their first project ?  \n",
    "\n",
    "Multiple features can affect the outcome for eg. total minutes visited, total lessons completed etc. We must determine the features to take into consideration. Also, these features can be correlated i.e. depend on each other.  \n",
    "\n",
    "This is where **machine learning** can help us. Various machine learning algorithms can be used to make predictions automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = [1, 2, 1, 3, 3, 1, 4, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  0.,  1.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb78690d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Data points\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.title(\"Sample histogram\")\n",
    "plt.hist(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example of `plt.hist`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C9RXRtkil4hNi+lNEJPrX5CzgwxTzMMYYE7BUK5bBqvpToNKfI+w04KimNlLV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\n2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cb7d101d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.mlab as mlab\n",
    "\n",
    "mu, sigma = 100, 15\n",
    "x = mu + sigma*np.random.randn(10000)\n",
    "\n",
    "# the histogram of the data\n",
    "n, bins, patches = plt.hist(x, 50, normed=1, facecolor='green', alpha=0.75)\n",
    "\n",
    "# add a 'best fit' line\n",
    "y = mlab.normpdf( bins, mu, sigma)\n",
    "l = plt.plot(bins, y, 'r--', linewidth=1)\n",
    "\n",
    "plt.xlabel('Smarts')\n",
    "plt.ylabel('Probability')\n",
    "plt.title(r'$\\mathrm{Histogram\\ of\\ IQ:}\\ \\mu=100,\\ \\sigma=15$')\n",
    "plt.axis([40, 160, 0, 0.03])\n",
    "plt.grid(True)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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