{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lecture 18 ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Student's lament ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = Table.read_table('scores_by_section.csv')\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores.group('Section')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores.group('Section', np.average).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_sample = scores.sample(27, with_replacement = False)\n",
    "random_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.average(random_sample.column('Midterm'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_sample = scores.sample(27, with_replacement = False)\n",
    "np.average(random_sample.column('Midterm'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "averages = make_array()\n",
    "\n",
    "for i in np.arange(50000):\n",
    "    random_sample = scores.sample(27, with_replacement = False)\n",
    "    new_average = np.average(random_sample.column('Midterm'))\n",
    "    averages = np.append(averages, new_average)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "observed_average = 13.6667"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Table().with_column('Random Sample Average', averages).hist(bins = 25)\n",
    "plots.scatter(observed_average, 0, color = 'red', s=40);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.count_nonzero(averages <= observed_average) / 50000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.count_nonzero(averages <= 13.6) / 50000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Table().with_column('Random Sample Average', averages).hist(bins = 25)\n",
    "plots.scatter(observed_average, 0, color='red', s=30)\n",
    "plots.plot([13.6, 13.6], [0, 0.35], color='gold', lw=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "language_info": {
   "codemirror_mode": {
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