datasciecne(mean median Mode).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Data Science\n",
    "Gathering the things with us\n",
    "http://media.sundog-soft.com/Udemy/DataScience.zip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "### statistics and probability"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "types of data\n",
    "\n",
    "1. numerical\n",
    "2. categorical no mathematical meaning(gender)\n",
    "3. ordinal numerical+categorical like movie ratings\n",
    "\n",
    "variance- spread of the data\n",
    "sigma squared=(average of squared differences from the mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean Median Mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean of average incomde and median "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mode is most common number of occurences of data"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "variance- spread of the data\n",
    "sigma squared=(average of squared differences from the mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "num=[1,4,5,4,8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 5, 4, 8]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean=np.array(num).sum()/5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.4"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "differences_from_mean=list(map(lambda x:x-3,num))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2, 1, 2, 1, 5]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "differences_from_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "square_of_diff=list(map(lambda x:x*x,differences_from_mean))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 1, 4, 1, 25]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "square_of_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "variance=np.array(square_of_diff).sum()/5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "standard_deviation=variance**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6457513110645907"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standard_deviation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "datapoints one standard_deviation away are called outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "plotting histogram of our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "num=np.random.normal(1,100,10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  2.,   2.,   2.,   8.,   7.,   7.,  20.,  21.,  40.,  49.,  65.,\n",
       "        114., 151., 172., 195., 257., 316., 384., 450., 452., 524., 618.,\n",
       "        587., 602., 647., 590., 595., 559., 471., 380., 360., 321., 254.,\n",
       "        198., 168., 123.,  78.,  72.,  44.,  33.,  15.,  12.,  12.,   5.,\n",
       "          7.,   3.,   4.,   3.,   0.,   1.]),\n",
       " array([-365.42435536, -350.07816746, -334.73197956, -319.38579166,\n",
       "        -304.03960376, -288.69341587, -273.34722797, -258.00104007,\n",
       "        -242.65485217, -227.30866427, -211.96247638, -196.61628848,\n",
       "        -181.27010058, -165.92391268, -150.57772479, -135.23153689,\n",
       "        -119.88534899, -104.53916109,  -89.19297319,  -73.8467853 ,\n",
       "         -58.5005974 ,  -43.1544095 ,  -27.8082216 ,  -12.4620337 ,\n",
       "           2.88415419,   18.23034209,   33.57652999,   48.92271789,\n",
       "          64.26890578,   79.61509368,   94.96128158,  110.30746948,\n",
       "         125.65365738,  140.99984527,  156.34603317,  171.69222107,\n",
       "         187.03840897,  202.38459687,  217.73078476,  233.07697266,\n",
       "         248.42316056,  263.76934846,  279.11553635,  294.46172425,\n",
       "         309.80791215,  325.15410005,  340.50028795,  355.84647584,\n",
       "         371.19266374,  386.53885164,  401.88503954]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 16,
     "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(num,50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1 and 8 are outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.random.randint(1,50,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModeResult(mode=array([17]), count=array([4]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mode(x)"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}