{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Standard Deviation and Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "incomes = np.random.normal(100.0, 50.0, 10000)\n",
    "\n",
    "plt.hist(incomes, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.99142414514945"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "incomes.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2499.1424880602317"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "incomes.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Experiment with different parameters on the normal function, and see what effect it has on the shape of the distribution. How does that new shape relate to the standard deviation and variance?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}