T2-2-Data Cleaning-Funciones de distribución de probabilidad.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Funciones de distribución de probabilidades"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGBA size=600x400 at 0x7F99CD305CC0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "import requests\n",
    "from io import BytesIO\n",
    "\n",
    "response = requests.get('http://work.thaslwanter.at/Stats/html/_images/PDF_CDF.png')\n",
    "img = Image.open(BytesIO(response.content))\n",
    "img.resize((600,400))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribución uniforme\n",
    "\n",
    "Entre un valor a y b, todo es igual de equiprobable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=1\n",
    "b=100\n",
    "n=1000000 #La uniformidad depende de la cantidad de datos\n",
    "data=np.random.uniform(a,b,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([90.26598382, 97.62405801, 19.91467969, ..., 44.96543543,\n",
       "       85.93488061, 89.80144535])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 99739., 100287., 100052.,  99350.,  99480., 100132.,  99934.,\n",
       "        100158., 100245., 100623.]),\n",
       " array([ 1.00007316, 10.90004452, 20.80001589, 30.69998726, 40.59995862,\n",
       "        50.49992999, 60.39990135, 70.29987272, 80.19984409, 90.09981545,\n",
       "        99.99978682]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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.hist(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La ley de los grandes número indica que a medida que hay más datos, existe una probabilidad mayor de obtener una distribución normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribución normal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=range(1000000)\n",
    "data=np.random.randn(1000000)\n",
    "\n",
    "fig,[ax1,ax2,ax3]=plt.subplots(1,3,figsize=(12,5))\n",
    "ax1.plot(x,data)\n",
    "\n",
    "ax2.hist(data)\n",
    "\n",
    "ax3.plot(x,sorted(data))\n",
    "\n",
    "plt.subplots_adjust(wspace=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estandarización\n",
    "\n",
    "Lo siguiente da una distribución normal N(0,1)\n",
    "\n",
    "\\begin{equation}\n",
    "s=\\frac{X-\\mu}{\\sigma}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  10.,   60.,  436., 1421., 2637., 2878., 1786.,  627.,  131.,\n",
       "          14.]),\n",
       " array([-4.29878442, -2.39136824, -0.48395206,  1.42346412,  3.3308803 ,\n",
       "         5.23829647,  7.14571265,  9.05312883, 10.96054501, 12.86796119,\n",
       "        14.77537737]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "mu=5.5\n",
    "sd=2.5\n",
    "data=5.5+2.5*np.random.randn(10000)# Teoría general del límite, tipicar, estandarizar.\n",
    "plt.hist(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando se especifican dos numeros entonces se generan los arrays con las longitudes especificadas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset=np.random.rand(4,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.69877695, 0.14503622, 0.39632711, 0.43404204, 0.14942959,\n",
       "        0.01092157],\n",
       "       [0.14220691, 0.82848461, 0.84400336, 0.8187253 , 0.56540107,\n",
       "        0.3466467 ],\n",
       "       [0.64287406, 0.04871338, 0.37231547, 0.88253958, 0.9506979 ,\n",
       "        0.29235458],\n",
       "       [0.44424997, 0.7551192 , 0.56897535, 0.0429038 , 0.91576983,\n",
       "        0.9557682 ]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La simulación de montecarlo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Generamos dos número aleatorios x e y entre 0 y 1\n",
    "* Calcularemos x^2+y^2\n",
    "    * Si el valor es inferior a 1 estamos dentro del círculo\n",
    "    * Si el valor es superior a 1 estamos fuera del círculo\n",
    "* Calculamos el número total de veces que cae dentro del círculo y lo dividimos entre el número total de intentos para obtener una aproximación de la probabilidad de caer dentro del círculo\n",
    "* Usamos dicha probabilidad para aproximar el valor de \\pi\n",
    "* Repetimos el experimento un número de veces (ejemplo 1000), para obtener (1000) diferentes aproximaciones de \\pi\n",
    "* Calculamos el promedio de los experimentos anteriores para un valor final de \\pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pi_montecarlo(n,n_exp):\n",
    "    '''n: Número de intentos en cada experimento\n",
    "    n_exp: Número de experimentos'''\n",
    "    pi_avg=0 \n",
    "    pi_value_list=[]\n",
    "    for i in range(n_exp): #Número de veces que se repite el experimento \n",
    "        value=0\n",
    "        x=np.random.uniform(0,1,n).tolist() #Todos los puntos tienen igual probabilidad\n",
    "        y=np.random.uniform(0,1,n).tolist() #Todos los puntos tienen igual probabilidad\n",
    "        for j in range(n):\n",
    "            z=np.sqrt((x[j]**2)+(y[j]**2))\n",
    "            if z<=1:\n",
    "                value+=1\n",
    "        float_value=float(value)\n",
    "        pi_value=(float_value*4)/n\n",
    "        pi_value_list.append(pi_value)\n",
    "        pi_avg+=pi_value\n",
    "    pi=pi_avg/n_exp\n",
    "    print(\"El valor de pi es: \"+str(pi))\n",
    "    fig=plt.plot(pi_value_list)\n",
    "    return (pi,fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El valor de pi es: 3.1408099999999974\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3.1408099999999974, [<matplotlib.lines.Line2D at 0x7f3afe694438>])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "pi_montecarlo(1000,400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=10000\n",
    "data=pd.DataFrame({\"A\":np.random.randn(n),\n",
    "                  \"B\":1.5+2.5*np.random.randn(n),\n",
    "                 \"C\":np.random.uniform(5,32,n)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.000035</td>\n",
       "      <td>1.505909</td>\n",
       "      <td>18.642312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.998237</td>\n",
       "      <td>2.534347</td>\n",
       "      <td>7.799760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.725212</td>\n",
       "      <td>-7.571301</td>\n",
       "      <td>5.000860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.674251</td>\n",
       "      <td>-0.181916</td>\n",
       "      <td>11.968859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.004863</td>\n",
       "      <td>1.486463</td>\n",
       "      <td>18.734213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.675318</td>\n",
       "      <td>3.210706</td>\n",
       "      <td>25.348714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.678328</td>\n",
       "      <td>11.308624</td>\n",
       "      <td>31.999695</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  A             B             C\n",
       "count  10000.000000  10000.000000  10000.000000\n",
       "mean       0.000035      1.505909     18.642312\n",
       "std        0.998237      2.534347      7.799760\n",
       "min       -3.725212     -7.571301      5.000860\n",
       "25%       -0.674251     -0.181916     11.968859\n",
       "50%        0.004863      1.486463     18.734213\n",
       "75%        0.675318      3.210706     25.348714\n",
       "max        3.678328     11.308624     31.999695"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,(ax1,ax2,ax3)=plt.subplots(1,3,figsize=(10,6))\n",
    "ax1.hist(data.A)\n",
    "ax2.hist(data.B)\n",
    "ax3.hist(data.C)\n",
    "plt.subplots_adjust(wspace=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_churn=pd.read_csv('../GitHub/python-ml-course/datasets/customer-churn-model/Customer Churn Model.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>State</th>\n",
       "      <th>Account Length</th>\n",
       "      <th>Area Code</th>\n",
       "      <th>Phone</th>\n",
       "      <th>Int'l Plan</th>\n",
       "      <th>VMail Plan</th>\n",
       "      <th>VMail Message</th>\n",
       "      <th>Day Mins</th>\n",
       "      <th>Day Calls</th>\n",
       "      <th>Day Charge</th>\n",
       "      <th>...</th>\n",
       "      <th>Eve Calls</th>\n",
       "      <th>Eve Charge</th>\n",
       "      <th>Night Mins</th>\n",
       "      <th>Night Calls</th>\n",
       "      <th>Night Charge</th>\n",
       "      <th>Intl Mins</th>\n",
       "      <th>Intl Calls</th>\n",
       "      <th>Intl Charge</th>\n",
       "      <th>CustServ Calls</th>\n",
       "      <th>Churn?</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>KS</td>\n",
       "      <td>128</td>\n",
       "      <td>415</td>\n",
       "      <td>382-4657</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>25</td>\n",
       "      <td>265.1</td>\n",
       "      <td>110</td>\n",
       "      <td>45.07</td>\n",
       "      <td>...</td>\n",
       "      <td>99</td>\n",
       "      <td>16.78</td>\n",
       "      <td>244.7</td>\n",
       "      <td>91</td>\n",
       "      <td>11.01</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.70</td>\n",
       "      <td>1</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>OH</td>\n",
       "      <td>107</td>\n",
       "      <td>415</td>\n",
       "      <td>371-7191</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>26</td>\n",
       "      <td>161.6</td>\n",
       "      <td>123</td>\n",
       "      <td>27.47</td>\n",
       "      <td>...</td>\n",
       "      <td>103</td>\n",
       "      <td>16.62</td>\n",
       "      <td>254.4</td>\n",
       "      <td>103</td>\n",
       "      <td>11.45</td>\n",
       "      <td>13.7</td>\n",
       "      <td>3</td>\n",
       "      <td>3.70</td>\n",
       "      <td>1</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NJ</td>\n",
       "      <td>137</td>\n",
       "      <td>415</td>\n",
       "      <td>358-1921</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>243.4</td>\n",
       "      <td>114</td>\n",
       "      <td>41.38</td>\n",
       "      <td>...</td>\n",
       "      <td>110</td>\n",
       "      <td>10.30</td>\n",
       "      <td>162.6</td>\n",
       "      <td>104</td>\n",
       "      <td>7.32</td>\n",
       "      <td>12.2</td>\n",
       "      <td>5</td>\n",
       "      <td>3.29</td>\n",
       "      <td>0</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>OH</td>\n",
       "      <td>84</td>\n",
       "      <td>408</td>\n",
       "      <td>375-9999</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>299.4</td>\n",
       "      <td>71</td>\n",
       "      <td>50.90</td>\n",
       "      <td>...</td>\n",
       "      <td>88</td>\n",
       "      <td>5.26</td>\n",
       "      <td>196.9</td>\n",
       "      <td>89</td>\n",
       "      <td>8.86</td>\n",
       "      <td>6.6</td>\n",
       "      <td>7</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OK</td>\n",
       "      <td>75</td>\n",
       "      <td>415</td>\n",
       "      <td>330-6626</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>166.7</td>\n",
       "      <td>113</td>\n",
       "      <td>28.34</td>\n",
       "      <td>...</td>\n",
       "      <td>122</td>\n",
       "      <td>12.61</td>\n",
       "      <td>186.9</td>\n",
       "      <td>121</td>\n",
       "      <td>8.41</td>\n",
       "      <td>10.1</td>\n",
       "      <td>3</td>\n",
       "      <td>2.73</td>\n",
       "      <td>3</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",
       "      <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",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3328</th>\n",
       "      <td>AZ</td>\n",
       "      <td>192</td>\n",
       "      <td>415</td>\n",
       "      <td>414-4276</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>36</td>\n",
       "      <td>156.2</td>\n",
       "      <td>77</td>\n",
       "      <td>26.55</td>\n",
       "      <td>...</td>\n",
       "      <td>126</td>\n",
       "      <td>18.32</td>\n",
       "      <td>279.1</td>\n",
       "      <td>83</td>\n",
       "      <td>12.56</td>\n",
       "      <td>9.9</td>\n",
       "      <td>6</td>\n",
       "      <td>2.67</td>\n",
       "      <td>2</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3329</th>\n",
       "      <td>WV</td>\n",
       "      <td>68</td>\n",
       "      <td>415</td>\n",
       "      <td>370-3271</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>231.1</td>\n",
       "      <td>57</td>\n",
       "      <td>39.29</td>\n",
       "      <td>...</td>\n",
       "      <td>55</td>\n",
       "      <td>13.04</td>\n",
       "      <td>191.3</td>\n",
       "      <td>123</td>\n",
       "      <td>8.61</td>\n",
       "      <td>9.6</td>\n",
       "      <td>4</td>\n",
       "      <td>2.59</td>\n",
       "      <td>3</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3330</th>\n",
       "      <td>RI</td>\n",
       "      <td>28</td>\n",
       "      <td>510</td>\n",
       "      <td>328-8230</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>180.8</td>\n",
       "      <td>109</td>\n",
       "      <td>30.74</td>\n",
       "      <td>...</td>\n",
       "      <td>58</td>\n",
       "      <td>24.55</td>\n",
       "      <td>191.9</td>\n",
       "      <td>91</td>\n",
       "      <td>8.64</td>\n",
       "      <td>14.1</td>\n",
       "      <td>6</td>\n",
       "      <td>3.81</td>\n",
       "      <td>2</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3331</th>\n",
       "      <td>CT</td>\n",
       "      <td>184</td>\n",
       "      <td>510</td>\n",
       "      <td>364-6381</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>213.8</td>\n",
       "      <td>105</td>\n",
       "      <td>36.35</td>\n",
       "      <td>...</td>\n",
       "      <td>84</td>\n",
       "      <td>13.57</td>\n",
       "      <td>139.2</td>\n",
       "      <td>137</td>\n",
       "      <td>6.26</td>\n",
       "      <td>5.0</td>\n",
       "      <td>10</td>\n",
       "      <td>1.35</td>\n",
       "      <td>2</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3332</th>\n",
       "      <td>TN</td>\n",
       "      <td>74</td>\n",
       "      <td>415</td>\n",
       "      <td>400-4344</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>25</td>\n",
       "      <td>234.4</td>\n",
       "      <td>113</td>\n",
       "      <td>39.85</td>\n",
       "      <td>...</td>\n",
       "      <td>82</td>\n",
       "      <td>22.60</td>\n",
       "      <td>241.4</td>\n",
       "      <td>77</td>\n",
       "      <td>10.86</td>\n",
       "      <td>13.7</td>\n",
       "      <td>4</td>\n",
       "      <td>3.70</td>\n",
       "      <td>0</td>\n",
       "      <td>False.</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3333 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     State  Account Length  Area Code     Phone Int'l Plan VMail Plan  \\\n",
       "0       KS             128        415  382-4657         no        yes   \n",
       "1       OH             107        415  371-7191         no        yes   \n",
       "2       NJ             137        415  358-1921         no         no   \n",
       "3       OH              84        408  375-9999        yes         no   \n",
       "4       OK              75        415  330-6626        yes         no   \n",
       "...    ...             ...        ...       ...        ...        ...   \n",
       "3328    AZ             192        415  414-4276         no        yes   \n",
       "3329    WV              68        415  370-3271         no         no   \n",
       "3330    RI              28        510  328-8230         no         no   \n",
       "3331    CT             184        510  364-6381        yes         no   \n",
       "3332    TN              74        415  400-4344         no        yes   \n",
       "\n",
       "      VMail Message  Day Mins  Day Calls  Day Charge  ...  Eve Calls  \\\n",
       "0                25     265.1        110       45.07  ...         99   \n",
       "1                26     161.6        123       27.47  ...        103   \n",
       "2                 0     243.4        114       41.38  ...        110   \n",
       "3                 0     299.4         71       50.90  ...         88   \n",
       "4                 0     166.7        113       28.34  ...        122   \n",
       "...             ...       ...        ...         ...  ...        ...   \n",
       "3328             36     156.2         77       26.55  ...        126   \n",
       "3329              0     231.1         57       39.29  ...         55   \n",
       "3330              0     180.8        109       30.74  ...         58   \n",
       "3331              0     213.8        105       36.35  ...         84   \n",
       "3332             25     234.4        113       39.85  ...         82   \n",
       "\n",
       "      Eve Charge  Night Mins  Night Calls  Night Charge  Intl Mins  \\\n",
       "0          16.78       244.7           91         11.01       10.0   \n",
       "1          16.62       254.4          103         11.45       13.7   \n",
       "2          10.30       162.6          104          7.32       12.2   \n",
       "3           5.26       196.9           89          8.86        6.6   \n",
       "4          12.61       186.9          121          8.41       10.1   \n",
       "...          ...         ...          ...           ...        ...   \n",
       "3328       18.32       279.1           83         12.56        9.9   \n",
       "3329       13.04       191.3          123          8.61        9.6   \n",
       "3330       24.55       191.9           91          8.64       14.1   \n",
       "3331       13.57       139.2          137          6.26        5.0   \n",
       "3332       22.60       241.4           77         10.86       13.7   \n",
       "\n",
       "      Intl Calls  Intl Charge  CustServ Calls  Churn?  \n",
       "0              3         2.70               1  False.  \n",
       "1              3         3.70               1  False.  \n",
       "2              5         3.29               0  False.  \n",
       "3              7         1.78               2  False.  \n",
       "4              3         2.73               3  False.  \n",
       "...          ...          ...             ...     ...  \n",
       "3328           6         2.67               2  False.  \n",
       "3329           4         2.59               3  False.  \n",
       "3330           6         3.81               2  False.  \n",
       "3331          10         1.35               2  False.  \n",
       "3332           4         3.70               0  False.  \n",
       "\n",
       "[3333 rows x 21 columns]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_churn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols_names=data_churn.columns.values.tolist()\n",
    "a=len(cols_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_data=pd.DataFrame({\"Column_names\":cols_names,\"A\":np.random.randn(a),\"B\":np.random.uniform(0,1,a)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Column_names</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>State</td>\n",
       "      <td>1.252381</td>\n",
       "      <td>0.303095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Account Length</td>\n",
       "      <td>1.074154</td>\n",
       "      <td>0.552665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Area Code</td>\n",
       "      <td>-2.564756</td>\n",
       "      <td>0.506561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Phone</td>\n",
       "      <td>-1.292558</td>\n",
       "      <td>0.522947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Int'l Plan</td>\n",
       "      <td>0.409160</td>\n",
       "      <td>0.097261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>VMail Plan</td>\n",
       "      <td>-0.756116</td>\n",
       "      <td>0.953373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>VMail Message</td>\n",
       "      <td>-0.033491</td>\n",
       "      <td>0.038108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Day Mins</td>\n",
       "      <td>0.369336</td>\n",
       "      <td>0.531087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Day Calls</td>\n",
       "      <td>1.282790</td>\n",
       "      <td>0.618594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Day Charge</td>\n",
       "      <td>0.342296</td>\n",
       "      <td>0.126899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Eve Mins</td>\n",
       "      <td>-2.200870</td>\n",
       "      <td>0.980844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Eve Calls</td>\n",
       "      <td>-0.447240</td>\n",
       "      <td>0.549362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Eve Charge</td>\n",
       "      <td>-1.278698</td>\n",
       "      <td>0.019222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Night Mins</td>\n",
       "      <td>-0.102974</td>\n",
       "      <td>0.206838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Night Calls</td>\n",
       "      <td>-0.042196</td>\n",
       "      <td>0.935101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Night Charge</td>\n",
       "      <td>2.064980</td>\n",
       "      <td>0.639894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Intl Mins</td>\n",
       "      <td>0.056300</td>\n",
       "      <td>0.845154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Intl Calls</td>\n",
       "      <td>-1.799829</td>\n",
       "      <td>0.707195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Intl Charge</td>\n",
       "      <td>0.673133</td>\n",
       "      <td>0.503564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>CustServ Calls</td>\n",
       "      <td>0.557518</td>\n",
       "      <td>0.506975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Churn?</td>\n",
       "      <td>0.130025</td>\n",
       "      <td>0.537225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Column_names         A         B\n",
       "0            State  1.252381  0.303095\n",
       "1   Account Length  1.074154  0.552665\n",
       "2        Area Code -2.564756  0.506561\n",
       "3            Phone -1.292558  0.522947\n",
       "4       Int'l Plan  0.409160  0.097261\n",
       "5       VMail Plan -0.756116  0.953373\n",
       "6    VMail Message -0.033491  0.038108\n",
       "7         Day Mins  0.369336  0.531087\n",
       "8        Day Calls  1.282790  0.618594\n",
       "9       Day Charge  0.342296  0.126899\n",
       "10        Eve Mins -2.200870  0.980844\n",
       "11       Eve Calls -0.447240  0.549362\n",
       "12      Eve Charge -1.278698  0.019222\n",
       "13      Night Mins -0.102974  0.206838\n",
       "14     Night Calls -0.042196  0.935101\n",
       "15    Night Charge  2.064980  0.639894\n",
       "16       Intl Mins  0.056300  0.845154\n",
       "17      Intl Calls -1.799829  0.707195\n",
       "18     Intl Charge  0.673133  0.503564\n",
       "19  CustServ Calls  0.557518  0.506975\n",
       "20          Churn?  0.130025  0.537225"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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