Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Fri Jun 28, 2019\n",
    "\n",
    "@author: Ruchika\n",
    "\"\"\"\n",
    "\n",
    "from collections import Counter\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "num_friends = [100.0,49,41,40,25,21,21,19,19,18,18,16,15,15,15,15,14,14,13,13,13,13,12,12,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]\n",
    "friend_counts = Counter(num_friends)#Create a dictionary with friend_number as key and its count as value\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": [
    "######################################################################################\n",
    "###########################       Histogram plot    #################################\n",
    "######################################################################################\n",
    "\n",
    "xs = [x for x in range(101)]#Largest value is 100\n",
    "ys = [friend_counts[x] for x in xs]\n",
    "plt.figure\n",
    "plt.bar(xs,ys)\n",
    "plt.axis([0,101,0,25])\n",
    "plt.title('Histogram of Friend Counts')\n",
    "plt.xlabel('# of friends')\n",
    "plt.ylabel('# of people')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find number of points\n",
    "num_points = len(num_friends)\n",
    "largest_value = max(num_friends)# Largest value\n",
    "smallest_value = min(num_friends)# Smallest value\n",
    "\n",
    "sorted_values = sorted(num_friends)#Sorted values\n",
    "smallest_value = sorted_values[0]\n",
    "second_smallest_value = sorted_values[1]\n",
    "second_largest_value = sorted_values[-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "###########################   Find mean of dataponts  ################################\n",
    "######################################################################################\n",
    "\n",
    "from typing import List\n",
    "\n",
    "#Find mean of the data\n",
    "def mean(xs: List[float]) -> float:\n",
    "    return sum(xs)/len(xs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.333333333333333"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "###########################   Find median of dataponts  ################################\n",
    "######################################################################################\n",
    "\n",
    "def _median_odd(xs: List[float]) -> float:\n",
    "    #If the length of xs is odd, median is the middle value after sorting the array\n",
    "    return (sorted(xs)[len(xs)//2])\n",
    "\n",
    "def _median_even(xs: List[float]) -> float:\n",
    "    #If the length of xs is even, median is the average of the sorted middle two elements\n",
    "    idx = len(xs)//2    \n",
    "    return (sum(sorted(xs)[idx-1:idx+1])*0.5)\n",
    "\n",
    "def median(v: List[float]) -> float:\n",
    "    return _median_even(v) if len(v)%2 == 0 else _median_odd(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median([1,10,2,9,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median([1,5,2,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################################################################################\n",
    "#####################   Returns the certain percentile (p) of the data  ##############\n",
    "######################################################################################\n",
    "\n",
    "def quantile(xs:  List[float], p:float)-> float:\n",
    "    p_index = int(p*len(xs))\n",
    "    return sorted(xs)[p_index]\n",
    "\n",
    "\n",
    "# Call function\n",
    "quantile(num_friends,0.1)\n",
    "quantile(num_friends,0.5)\n",
    "quantile(num_friends,0.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "###########################   Find mode of dataponts  ################################\n",
    "######################################################################################\n",
    "\n",
    "def mode(x: List[float]) -> float:\n",
    "    counts = Counter(x)\n",
    "    max_count = max(counts.values())\n",
    "    return [x_i for x_i, count in counts.items() if count == max_count]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 1]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mode(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "##########    Dispersion of the data can be measured using range  ###################\n",
    "######################################################################################\n",
    "\n",
    "def data_range(xs: List[float])-> float:\n",
    "    return max(xs) - min(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_range(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "##########    A more complex measure of dispersion of data is variance  ##############\n",
    "######################################################################################\n",
    "\n",
    "def de_mean(xs: List[float]) -> float:\n",
    "    #Subtract mean from each element of xs\n",
    "    x_bar = mean(xs)\n",
    "    return [x-x_bar for x in xs]\n",
    "\n",
    "def variance(xs: List[float]) -> float:\n",
    "    #Almost the average squared deviation from the mean\n",
    "    assert(len(xs)>=2),\"variance requires atleast two elements\"\n",
    "    sum_of_squares = sum(x*x for x in de_mean(xs))\n",
    "    return sum_of_squares/(len(xs)-1)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "81.54351395730716"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variance(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.03014473623248"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################################################################################\n",
    "########## Dispersion of data can also be quantified using standard deviation  #######\n",
    "######################################################################################\n",
    "\n",
    "import math\n",
    "\n",
    "def standard_deviation(xs: List[float]) -> float:\n",
    "    #Standard deviation is the square root of variance\n",
    "    return math.sqrt(variance(xs))\n",
    "\n",
    "standard_deviation(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################################################################################\n",
    "###########################   Find interquantile range ################################\n",
    "######################################################################################\n",
    "\n",
    "def interquantile_range(xs: List[float])-> float:\n",
    "    #Returns the difference between the 75%-tile and the 25%-tile\n",
    "    return quantile(xs,0.75) - quantile(xs,0.25)\n",
    "\n",
    "interquantile_range(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "###########################   Find covariance of two vectors #########################\n",
    "######################################################################################\n",
    "daily_minutes = [1,68.77,51.25,52.08,38.36,44.54,57.13,51.4,41.42,31.22,34.76,54.01,38.79,47.59,49.1,27.66,41.03,36.73,48.65,28.12,46.62,35.57,32.98,35,26.07,23.77,39.73,40.57,31.65,31.21,36.32,20.45,21.93,26.02,27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,38.11,38.18,36.31,21.03,30.86,36.07,28.66,29.08,37.28,15.28,24.17,22.31,30.17,25.53,19.85,35.37,44.6,17.23,13.47,26.33,35.02,32.09,24.81,19.33,28.77,24.26,31.98,25.73,24.86,16.28,34.51,15.23,39.72,40.8,26.06,35.76,34.76,16.13,44.04,18.03,19.65,32.62,35.59,39.43,14.18,35.24,40.13,41.82,35.45,36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,26.89,23.48,8.38,27.81,32.35,23.84]\n",
    "\n",
    "def covariance(xs: List[float], ys: List[float])-> float:\n",
    "    sum_of_squares = sum(x*y for x,y in zip(de_mean(xs),de_mean(ys)))\n",
    "    return sum_of_squares/(len(xs)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.425435139573064"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covariance(num_friends,daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "######################################################################################\n",
    "############## Correlation is unitless and always lies between #######################\n",
    "################-1 (perfect anticorrelation) & 1 (perfect correlation)################\n",
    "######################################################################################\n",
    "\n",
    "def correlation(xs: List[float], ys: List[float])-> float:\n",
    "    stdev_x = standard_deviation(xs)\n",
    "    stdev_y = standard_deviation(ys)\n",
    "    if stdev_x>0 and stdev_y>0:\n",
    "        return covariance(xs,ys)/stdev_x/stdev_y\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24736957366478218"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(num_friends,daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZsPdovsDM2s1stZndFC3vY2bLzexhM7sqmg+58cRZWatkZ2XRInjve8PzcHL8lKrM04q7ura3a9CYiIxaxSsCd3czux74y1F8x2eAB4GdouVvAt9x9yvN7PvAScCFo/j82uvrg4GBEAQGBsqfcS9aBP/0T+H1rbcWJqdJc4Y/mhHA6uoqIjWUJvvo3Wb2VyP5cDPbizDF5cXRshFyFV0TbbIEOHYkn52prq7C1JODg2G5lGuvHbo8MBDO8Ddvrn6GH1fmZ589sjb+7m444wwFAREZtTT3CA4DPmlmjwJ/IsxF4O7+lhT7LgTmAztGy13AJncfiJbXApNL7Whmc4m6qU6ZMiXFV9XQ6tWVl2PHHReuBIpVCh5JGrcgIg0gTSA4aiQfbGYfAJ5291Vm1hOvLrFpyUZ4d18ELIIwQ9lIyjBiTz5ZeTk2NxpOce21MGECLF0agkBbW0hPISLSBKo2Dbn7Y8DewOHR65fS7AccCnwwupK4ktAktBCYaGZxANoLWDeCcmdr990rLyfNnQu33ALz58P48eEG7vjxw7+Bq8lkRKROqlboZvYV4DTgjGjVOAoJ6Mpy9zPcfS93nwp8FPi5u38MuB34ULTZHOCGEZR7dKpVurNnh8rcLDzPnl19/9G0+cddSc88MzyPdTBQEBLJtTRNQ38DzADuAXD3dWa2Y+VdKjoNuNLMvg6sBi4ZxWcNX5r++93dcPvtpXvl9PfDYYcV9r/99qHZSUfS5l/PcQEanCaSe2kCwZaoG6kDmNlrh/sl7t4H9EWvHwEOHu5n1ExxpdvbW7rCL1ep9/aGXkEQnnt7R19x1nMyGQ1OE8m9NIHgajP7AaFt/xPAicBF2RYrQ8lKt6MDFi8OlWA9z4brOS5AM5qJ5F6apHPfMrMjgOeBNwFfdvfbMi9ZVpKV7uOPh0Fhg4OFvv/VKuEZMyovj6ZceQtCItIQ0uYauh/YgdDV8/7sijNG4ko3DgIQnjdtCjdNK1WIGzeG7qFxN9HVq6vvU06jZBDVeAaRXKsaCMzsZODLwM8J4wDON7OvufvirAuXueKBYv/xH+G5UjNRTw+MGxeaUtrbhzYtlZreshzdpBWRBpHmiuALwAx33whgZl3AL4HmDwTFA8W2bQvPlW4ix9u5F7aPm5ZOOSV9riHdpBWRBpEmEKwFXkgsvwA8kU1xxtizzw5dNgvNPR0dcNFFoZLu6IA77yxU0r29IacQhADQ3h4ebW1h+8HByhV73BzU1aWbtCLSENIEgj8Ay83sBsI9gmOAFWb2rwDu/u0My1c7ixaFVBDHHVdIDfHKK0O32X9/+PjH4eqrYc2asG5gAE4/Hc45J1TgxVcRRx8NBx8cKvZ58ypX7MXNQcNpShIRyUiaQPC76BGLRwKPZlDZ2CpOFw0hGJx0EqxYUdhu3ryw/jvfGbr/ffeFynrr1nCFMG5cCBCdnXDUUaEyP/DA8r1v4quAxx8f2hy0cWPIIJpWo9xcFpGWkqb76FfHoiCZKk4Xfe21ocJPJo1LXilMngwbNhS2b28PFTeEYHDssaWvApYt275iT14FdHSEz4LhNwfp5rKIZCRN8rjmN316+eU4aVwcBACmTh26/Y5FFz+77x4q/I0bq88ylrwpPDAAJ544snxEo5nRTESkgnzMWTxxYrgR7B5u6k6cWHn74myj06fD+vWFs/E4CV3xqNyuru3HFBRvM3v2yM7kNQJYRDJiXm1O3gYwc+ZMX7ly5fB3TPbQSTbhVLtJ299fuCcwblzh7LtS+3+pZqJ4u1q17esegYgMg5mtcveZ1bZLM6DsXODrwMvAz4CDgHnuXjUVdV3198O73lWozC+4IFT+lSrsZM+ivr7tK91SlW88KnfBgvLjAmo1clcjgEUkA2maht7j7vPN7G8IYwo+TJhToLEDwbnnhiAA4fnmm+G660KF/coroZnolVcKA8c2bQr7QOhZ9IMfDK9HT6WmG53Ji0gDSxMIxkXP7wOucPdnwxz0DW7dutLLmzaFIADh+aKLCq+TLrlkeH38yyVvU28fEWlwaQLBjWb2EKFp6F/MbBLwSpV96q+nZ+gYgfgMvbi3TZwmoq2oA9U998CqVYXKO9633D2CeH1xJa9UEiLS4NKMIzjdzL4JPO/u28zsJcLo4sZWrqfQa14zdLs4rURnJ5x6ahhRPGEC3Hjj0MlrFi8eevO4uzvd2b56+4hIg0tzs3gCcAowBZgL7AnsB9yUbdFGKVkBjxtXqIAPOCDkDoodc0wYHFbcnHPLLYXK+8knCwPK4sDQ3Z1utjPl+xeRBpemaehSYBXw19HyWuC/afRAAEOzhF5/PZx1VhgTMH58oZKfP7/0nMXJyru3t/Tn9/SEkcLx3AQXXxy+K3nVEH9eLQKAbjqLSAbSBII/d/e/M7PjAdz9ZWuGu8XJLKEDA0N7BM2fH5qKKlWoxZX3pZcWgseMGaH3UVdXaFqCQuZRGHrVUCu66SwiGUk1eb2ZxbOTYWZ/DmyutpOZvQa4Exgffc817v4VM9sHuBLYGbgH+Li7bxlh+csrzhKa1NcHy5en/6zubrj99u0HjsWpp8diUJ5uOotIRtLkGjqLMJBsbzO7HFgGnJZiv83A4e5+EDAdONLMDgG+CXzH3acBzwEnjaTgVRWniUjac8/hf153dyG/0ObNhdxBZuERJ5OL1Wou41h8z6O9XTedRaSm0vQautXMVgGHEKaq/Iy7P5NiPwdejBbHRQ8HDgf+Plq/hBBoLhx2yauZPbvQ06ejIzTbxO338+cXtku2u0P1NviurkITUPJKwH1oL6WNG2t7PLrpLCIZSdNraJm7zwJ+UmJdtX3bCTea3wh8jzCvwSZ3jxrvWQtMLrPvXEIvJaZMmVLtq7YX9+opVclDoY0/bubp6CjcWK7UBp+cvN4sPLuHR3t7YarKLM7YlWJCRDJQNhBEbfwTgF3M7PWEqwGAnQhdSKty923AdDObCFwHvLnUZmX2XQQsgpB0Ls33bae44oz7/h92WKGNP67It20rnNFXaoMvnrw+OW3l5z9f/Sa0iEiDqXRF8E/APEKlf09i/fOEs/vU3H2TmfURmpcmmllHdFWwF7Cu4s611tsb2vihMKo4VumMPpllNA4e8VVBctDacPITiYg0gLKBwN2/C3zXzE519/OH+8FRKoqtURDYAXg34Ubx7cCHCD2H5lCY+jJbcUVerjdRWxucfDJMmVI6jUTcdRMKASSevB50A1dEmlaa7qN/NLPZxSvdvcwoq1ftASyJ7hO0AVe7+01m9gBwpZl9HVgNXDLcQg9b8XSRHR2hMo+7f0Ko1GfMGDpTWSzZdbN4CMWhh4a0Fccdl645SIPCRKTBpAkEf5V4/RpgFqGpqGIgcPf7gO36ULr7I8DBwyjjyJWaNB7gE58IZ/4rVoQRx7Gbby6dcTSZriIOItu2hdd33x1e33VXmMC+UuVeaVCYAoSI1Ema7qOnJpfN7HXADzMrUa0kbwp3dBRuDHd0hDP/jRvh2WeH7nP99eHR0RHyEZXLFwSFAHPRRZVzDSWVGxSmUcMiUkcjmbP4JWBarQtSc8mbwlu3FtJMDw7Cpz5VGAxWSpyS4rrrCuvK9UBavLiQa2jx4srdT8tlItWoYRGpozTjCG6k0MWzDTgAuDrLQtVE8U3heBDYwMDQiWna2oYux4ontiknDibJnkTlKvNyg8KUqlpE6ijNFcG3Eq8HgMfcfW1G5amd4hQTyRQQyW6jb397YY6CW28trC/XfTRZgff1hauNeEBZW1sIDJUq81KDwjRqWETqKM09gjvGoiA1N3v20Iyh551XmLz+1FMLqSfim73JGcrM4Pnnw+jjuEIv1YafTDcxOAjHHw8bNoQeRFDYP+1UlwoAIlIHaZqG/pbQ/39XwuhiI6QS2injso1OMmNoqcr42mvDTGRLlxaadeI0Ex0dQ9v758wZOuF93OxTnG7iqqvCNnfckS5dhYhIA0jTNHQucLS7P5h1YWqu1Fl2f//QNNLJM/o4RURxb6AHHhh6H2HTpvC6p6cwyU08JmFwcGhSOt38FZEGlyYN9VNNGQTKSfbQSfYcamsLzUEQupd2dIT3OjrCVUDSmjXhubsbFi4MzUaf/WwICnGa6HHjlDJaRJpCmiuClWZ2FXA9iQlp3P3HmZUqC8lcQXFa6mTG0fZ2uOSSEBzi9RCep00Lg89i06cXPjO+urjrrhAU4gFpoJu/ItIU0gSCnQhjB96TWOdA4weCZOWfTDed7DVUaqrJrVsLyeS2bQs3gJPiG8nJEctbtsDq1WHEMujmr4g0jTS9hk4Yi4LUXH9/OBuPB5PFffyT7fdxCulSU03GvYg6O8MVQLJr6cUXF24qx91SOzoKVxSdneFGtQKBiDSBSvMRzHf3c83sfErMGeDun860ZKPV2zs0W2h7e3gkm4OKX8c5hMaNg/PPLzTz9PUN7R2UnKf46KPhpZfCfYQ77wzrNm+u/eT1IiIZqXRFEN8gXjkWBam54pHFhx4KRx5ZerayNFNVxr2DioPHT39aegL7cumuRUQaTKX5CG6MnpeMXXEytPPOQyeNKc4bVOp1cl21pHPFeYuKRzaLiDSoNAPKZgL/Brwhub27vyXDco1ecUU82oq5XNK5JUsKVwqDg4V7BLO3m8JBRKQhpek1dDnwBeB+YDDb4tTQjBnll5N5g2D43TyT+y9cGEYpH3dcmI9AXUZFpMmkCQQb3H1p5iWptWT6h7a2sAzbz1aWTAWRHAdQriIvt388jkBEpMmkCQRfMbOLgWU004Cynp7Q+2fLlvBcKvd/sivp5s1wyimFyevL5Qca7f4iIg0mTYqJE4DpwJHA0dHjA1kWqmZKzTMQ5/4vTgXR3h4q9uTkMKX09BTST7S3Fz473rfa/iIiDSbNFcFB7n5g5iWptb6+QrfObdsKid/K9QDq6oJPf7rQ5FMpP1AywMQjkJOBQfmFRKSJpAkEd5vZAe7+wHA+2Mz2JkxwvzvhJvMid/+ume0MXAVMBR4FPuLuzw2r1GkUz/rV1TV0foBSPYCSgaOcZIBxH1r5n3pqSEh33HFqFhKRppEmELwdmGNmvyfcI4jnI6jWfXQA+Jy732NmOwKrzOw24B+BZe5+jpmdDpwOnDbiIygneeafnIxm3LjSaaF7ewspJwYGyo8MLg4w8Q3mZD6ju+4KPYgUDESkCaQJBEeO5IPdfT2wPnr9gpk9CEwGjgF6os2WAH1kEQigcOb/z/9cSDexZcvI0j8ku4yWmlZywQJNQC8iTSlN0rnHRvslZjYVmAEsB3aLggTuvt7Mdi2zz1xgLsCUOKPnSBWne0guxxX8jBmFNBKdnWE5OVVlnMAuvqKIRyknM5xqAnoRaUJprghGxcz+DLgWmOfuz1txKoYy3H0RsAhg5syZJdKDDkOpUcULFgxtzime1zi5/r3vLX1FkRxTkHYcgohIg8k0EJjZOEIQuDwx7uApM9sjuhrYA3g6yzIAQyey7+iAn/wEbrhhaHrqLVvg5ptDJtEJE4Y286xbV/pzk2MKtmwJQSCZz0hEpAlkFggsnPpfAjzo7t9OvLUUmAOcEz3fkFUZXpWcyH7FCrj++rA+mZ66ra2wHgpzDXR2wkknwb33Fs784zxCPT2F8Qft7WoOEpGmlOUVwaHAx4H7zSya5JcvEgLA1WZ2EvA48OEMy7C9Z58dunzggbDrrvDEE/BgYmrmN70J9tordAWdO7d8HqG4qStlk5eISKPJLBC4+y8IXU1LmZXV95aUbMsvdv/94bmtaJD1b34Dv/710K6gxe3+fX2hq2k825l6ColIE8r8ZnFdxT16knMLt7UVmnOS9wgAjj22cI/gxhurdwUtHlOgpiERaUKtGwiKs4TGcwuXGwTW2Qnz5xd6A91yy9AKPjmOIA4KxekqdDUgIk2odQNBskcPwCc+AVOmbF9hl2r7L5WPKNlNNJlZtFSTkYhIE2ndQFDcbDNjRmFOgqQ0FXlxN1HdCxCRFtK6gaA411CyCajaXAH9/UNHEp9/vu4FiEjLSjMfQfPq7g4DvDZu3P6MvpLe3rCde3hevToEj7PP1oQzItJyWveKIKkWvXuSTUilbhyLiDSp1g4E5TKGwtCEcsWVerWJ78vdOBbAcKZFAAAKRElEQVQRaUKtGwhKVdhnnFF58vq4Ui838T3oxrGItJzWvUdQqsKO12/eXFi/dev22yTnJS6etrJ4zmPdOBaRJte6VwRxZT44OLQy7+oqjCSOp5oslTSuXA4hDSITkRbTuoEAhk4yH1u9uvQ2ZiHvUJySolIOIQ0iE5EW0rqBIDnJ/LZthcq8eLay+Opg61Y45ZSwfXFKinIpJkREWkDrBoLiLqNdXaGnULG4wm9rCwEjDgzJlBSgnkIi0rJaNxCUG1nc0RFGCw8MVJ6ecvZsTUwvIrnQuoEACm35CxaEnkKDg6HpZ+7c9AnoQOmmRaSltXYgiCV7Cg0OhgFic+duv125m8DqKSQiLSwfgaDSALG01FNIRFpU6w4oS+rpgfHjw43h8ePVtCMikpCPKwI17YiIlJVZIDCzxcAHgKfd/S+idTsDVwFTgUeBj7j7c1mVYQg17YiIlJRl09BlwJFF604Hlrn7NGBZtJyd/v7QY6i/P9OvERFpZpldEbj7nWY2tWj1MUBP9HoJ0AeclkkBimcZU99/EZGSxvpm8W7uvh4get41s28qnmWstzezrxIRaWYN22vIzOaa2UozW7lhw4bRf+CTT6qZSESkhLEOBE+Z2R4A0fPT5TZ090XuPtPdZ06aNGn43zR7dugqahaahn76UzjzzJAzSMFARORVYx0IlgJzotdzgBsy+6bu7pBH6Igj4P3vD3mC0k5eLyKSI1l2H72CcGN4FzNbC3wFOAe42sxOAh4HPpzV99PfPzTRXHFaaRERAbLtNXR8mbdmZfWdQySnqoShaaXVe0hE5FWtO7K4OGNoMq20iIi8qnUDgdJKiIik0rqBAJRWQkQkhYYdRyAiImNDgUBEJOcUCEREck6BQEQk5xQIRERyToFARCTnFAhERHJOgUBEJOcUCEREck6BQEQk5xQIRERyToFARCTnFAhERHJOgUBEJOcUCEREck6BQEQk5xQIREQaUX8/LFgQnjPW2jOUiYg0o/5+mDWrMOf6smWZzrZYlysCMzvSzH5tZr81s9PrUQYRkYbV1xeCwLZt4bmvL9OvG/NAYGbtwPeAo4ADgOPN7ICxLoeISMPq6QlXAu3t4bmnJ9Ovq0fT0MHAb939EQAzuxI4BnigDmUREWk83d2hOaivLwSBDJuFoD6BYDLwRGJ5LfC24o3MbC4wF2DKlCljUzIRkUbR3Z15AIjV4x6BlVjn261wX+TuM9195qRJk8agWCIi+VSPQLAW2DuxvBewrg7lEBER6hMI/geYZmb7mFkn8FFgaR3KISIi1OEegbsPmNmngFuAdmCxu//vWJdDRESCugwoc/efAj+tx3eLiMhQSjEhIpJz5r5dh52GY2YbgMeGscsuwDMZFadR5fGYIZ/Hncdjhnwe92iP+Q3uXrXbZVMEguEys5XuPrPe5RhLeTxmyOdx5/GYIZ/HPVbHrKYhEZGcUyAQEcm5Vg0Ei+pdgDrI4zFDPo87j8cM+TzuMTnmlrxHICIi6bXqFYGIiKSkQCAiknMtFQjyMvOZme1tZreb2YNm9r9m9plo/c5mdpuZPRw9v77eZa01M2s3s9VmdlO0vI+ZLY+O+aoof1VLMbOJZnaNmT0U/ebdrf5bm9lno3/bvzKzK8zsNa34W5vZYjN72sx+lVhX8re14LyofrvPzN5aq3K0TCDI2cxnA8Dn3P3NwCHAKdGxng4sc/dpwLJoudV8BngwsfxN4DvRMT8HnFSXUmXru8DP3H1/4CDC8bfsb21mk4FPAzPd/S8IOck+Smv+1pcBRxatK/fbHgVMix5zgQtrVYiWCQQkZj5z9y1APPNZy3H39e5+T/T6BULFMJlwvEuizZYAx9anhNkws72A9wMXR8sGHA5cE23Sise8E/BO4BIAd9/i7pto8d+akAdtBzPrACYA62nB39rd7wSeLVpd7rc9Buj14G5gopntUYtytFIgKDXz2eQ6lWXMmNlUYAawHNjN3ddDCBbArvUrWSYWAvOBwWi5C9jk7gPRciv+5vsCG4BLoyaxi83stbTwb+3ufwC+BTxOCAB/BFbR+r91rNxvm1kd10qBINXMZ63EzP4MuBaY5+7P17s8WTKzDwBPu/uq5OoSm7bab94BvBW40N1nAH+ihZqBSonaxI8B9gH2BF5LaBYp1mq/dTWZ/XtvpUCQq5nPzGwcIQhc7u4/jlY/FV8qRs9P16t8GTgU+KCZPUpo9juccIUwMWo+gNb8zdcCa919ebR8DSEwtPJv/W7g9+6+wd23Aj8G/prW/61j5X7bzOq4VgoEuZn5LGobvwR40N2/nXhrKTAnej0HuGGsy5YVdz/D3fdy96mE3/bn7v4x4HbgQ9FmLXXMAO7+JPCEme0XrZoFPEAL/9aEJqFDzGxC9G89PuaW/q0Tyv22S4HZUe+hQ4A/xk1Io+buLfMA3gf8Bvgd8G/1Lk+Gx/l2wiXhfcCa6PE+Qpv5MuDh6Hnnepc1o+PvAW6KXu8LrAB+C/w3ML7e5cvgeKcDK6Pf+3rg9a3+WwNfBR4CfgX8EBjfir81cAXhPshWwhn/SeV+W0LT0Pei+u1+Qq+qmpRDKSZERHKulZqGRERkBBQIRERyToFARCTnFAhERHJOgUBEJOcUCKQlmdkCM+sxs2OHm4nWzCZFWS5Xm9k7it57R5QVc42Z7VBi31+OtuzR50xNZqQUyZICgbSqtxHyL70LuGuY+84CHnL3Ge5evO/HgG+5+3R3fzleGWW/xd3/ehRlFqkLBQJpKWb272Z2H/BXQD9wMnChmX25xLZvMLNlUW73ZWY2xcymA+cC7ys+6zezk4GPAF82s8ujK47bzexHhAE+mNmLie2/YGb/E33+V6N1U6M5BS6Krixujb/DzP7SzO41s37glMTn/B8zWxGV5z4zm1b7v5zkWr1H1umhR60fhJTk5wPjgP9XYbsbgTnR6xOB66PX/whcUGafy4APRa97CEng9km8/2L0/B7CxONGOOG6iZBOeiphPonp0XZXA/8Qvb4PeFf0+t+BX0Wvzwc+Fr3uBHao999Yj9Z66IpAWtEMQtqN/Qk5asrpBn4Uvf4hIXXHcK1w99+XWP+e6LEauCcqS3wm/3t3XxO9XgVMNbPXARPd/Y5EeWL9wBfN7DTgDZ5okhKphY7qm4g0h6hZ5zJCVsZnCBOamJmtAbpTVKAjybfyp3LFARa4+w+KyjgV2JxYtQ3YIdq+5Pe7+4/MbDlhUp5bzOxkd//5CMoqUpKuCKRluPsad59OSDx4APBz4L1edGM34ZeETKYQbgL/oobFuQU4MZozAjObbGZlJ4/xMOvYH80svir5WPyeme0LPOLu5xEyUL6lhuUU0RWBtBYzmwQ85+6DZra/u1dqGvo0sNjMvkCYBeyEWpXD3W81szcD/SGTMi8C/0C4AijnhKg8LxECSezvgH8ws63Ak8DXalVOEUDZR0VE8k5NQyIiOadAICKScwoEIiI5p0AgIpJzCgQiIjmnQCAiknMKBCIiOff/Af3J4WG4QiYuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "######################################################################################\n",
    "######################  Plot distribution of the data ################################\n",
    "######################################################################################\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "plt.figure()\n",
    "plt.scatter(num_friends,daily_minutes,color='red',marker = '.')\n",
    "plt.title(\"Correlation with an outlier\")#Title\n",
    "plt.ylabel(\"minutes per day\")#Adding label to the y-axis\n",
    "plt.xlabel(\"# of friends\")#Adding label to the x-axis\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": [
    "# Correlation is very sensitive to outliers\n",
    "# Remove outlier\n",
    "\n",
    "outlier = num_friends.index(100) #Index of the outlier\n",
    "\n",
    "num_friends_good = [x\n",
    "                   for i, x in enumerate(num_friends)# i(index) and x(value)\n",
    "                   if i!=outlier]\n",
    "daily_minutes_good = [x\n",
    "                   for i, x in enumerate(daily_minutes)# i(index) and x(value)\n",
    "                   if i!=outlier]\n",
    "\n",
    "daily_hours_good = [dm/60 for dm in daily_minutes_good]\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(num_friends_good,daily_minutes_good,color='red',marker = '.')\n",
    "plt.title(\"Correlation with an outlier\")#Title\n",
    "plt.ylabel(\"minutes per day\")#Adding label to the y-axis\n",
    "plt.xlabel(\"# of friends\")#Adding label to the x-axis\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}