stats practice.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import helper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal Distribution Chart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_distribution1 = np.random.normal(69.1,2.9,(1000,1))\n",
    "random_distribution2 = np.random.normal(63.7,2.7,(1000,1))\n",
    "random_distributions = np.hstack((random_distribution1,random_distribution2))\n",
    "\n",
    "dist_df = pd.DataFrame(random_distributions)\n",
    "\n",
    "helper.distplot_w_stats(dist_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tem_df1 = dist_df[0].to_frame(name='x')\n",
    "tem_df2 = dist_df[1].to_frame(name='x')\n",
    "\n",
    "tem_df1['hue'] = 'male'\n",
    "tem_df2['hue'] = 'female'\n",
    "\n",
    "tem_df = pd.concat([tem_df1,tem_df2], axis=0)\n",
    "# cut into 40 bins,\n",
    "# select the mid of the interval\n",
    "# round to 2 digits\n",
    "tem_df['x'] = pd.cut(tem_df['x'],100).apply(lambda x: round(x.mid,0))\n",
    "\n",
    "# plot\n",
    "pal = dict(male=\"#6495ED\", female=\"#F08080\")\n",
    "\n",
    "plt.subplots(figsize=(12,8))\n",
    "sns.countplot(x='x',hue='hue',data=tem_df,palette=pal)\n",
    "plt.legend(loc=1)\n",
    "\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantile and its inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>69.111420</td>\n",
       "      <td>63.734869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.903791</td>\n",
       "      <td>2.685784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>59.934842</td>\n",
       "      <td>55.309648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>67.191952</td>\n",
       "      <td>61.860614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>69.115828</td>\n",
       "      <td>63.754128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>71.014586</td>\n",
       "      <td>65.623260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>78.921817</td>\n",
       "      <td>71.995975</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1\n",
       "count  1000.000000  1000.000000\n",
       "mean     69.111420    63.734869\n",
       "std       2.903791     2.685784\n",
       "min      59.934842    55.309648\n",
       "25%      67.191952    61.860614\n",
       "50%      69.115828    63.754128\n",
       "75%      71.014586    65.623260\n",
       "max      78.921817    71.995975"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The list above shows the information of quantiles of the data. The 50% quantile of the data is the median.\n",
    "\n",
    "We know that quantile is a function to divide the data into equally split groups. To prove each quantile contains the same amount of the data, let's test the quantile function in pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250\n",
      "500\n",
      "750\n"
     ]
    }
   ],
   "source": [
    "for quantile in [67.191952, 69.115828, 71.014586]:\n",
    "    count = (dist_df[0] < quantile).sum()\n",
    "    print(count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**To know the top 2.2% of people's height.**\n",
    "\n",
    "Solution: pandas.DataFrame.quantile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The top 2.2% of people's height is 74.95986100184189\n"
     ]
    }
   ],
   "source": [
    "# To get top 2.2% of people's height\n",
    "x = dist_df[0].quantile(.978)\n",
    "print(\"The top 2.2% of people's height is {}\".format(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Knowing the height of someone, figure out his/her percentile in the population.**\n",
    "\n",
    "Solution: Scipy.stats.percentileofscore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Knowing the quantile (y=0.3),\n",
      "using the pandas quantile function we know the 30.0th percentile is: 67.6939389226526\n",
      "------------------------------\n",
      "Knowing the value (x=67.6939389226526),\n",
      "using the scipy percentile function we know the quantile of this value is: 30.0\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "#quantile function\n",
    "y = .30 # change this to test the result\n",
    "x = dist_df.quantile(y)[0]\n",
    "print(\"Knowing the quantile (y={}),\\nusing the pandas quantile function we know the {}th percentile is: {}\".format(y,y*100,x))\n",
    "\n",
    "print(\"-\"*30)\n",
    "\n",
    "#inverse of quantile\n",
    "z = stats.percentileofscore(dist_df[0],x)\n",
    "print(\"Knowing the value (x={}),\\nusing the scipy percentile function we know the quantile of this value is: {}\".format(x,z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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