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   "cell_type": "markdown",
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   "source": [
    "# Data Spread\n",
    "\n",
    "1. Mean \n",
    "2. Stardard Deviation\n",
    "3. Variance\n",
    "\n",
    "##### ---------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.14.2\n",
      "0.20.3\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "\n",
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "\n",
    "print np.__version__\n",
    "print pd.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python Way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mean(x):\n",
    "    return sum(x) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def variance(x):\n",
    "    return (standard_deviation(x))**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def standard_deviation(lst):\n",
    "    m = mean(lst)\n",
    "    return math.sqrt(float(reduce(lambda x, y: x + y, map(lambda x: (x - m) ** 2, lst))) / len(lst))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 3.0\n",
      "Variance: 2.0\n",
      "Standard Deviation: 1.41421356237\n"
     ]
    }
   ],
   "source": [
    "X = [1, 2, 3, 4, 5]\n",
    "print 'Mean: {}'.format(mean(X))\n",
    "print 'Variance: {}'.format(variance(X))\n",
    "print 'Standard Deviation: {}'.format(standard_deviation(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy Way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mean(x):\n",
    "    return np.mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def variance(x):\n",
    "    return np.var(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def standard_deviation(x):\n",
    "    return np.std(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 3.0\n",
      "Variance: 2.0\n",
      "Standard Deviation: 1.41421356237\n"
     ]
    }
   ],
   "source": [
    "X = [1, 2, 3, 4, 5]\n",
    "print 'Mean: {}'.format(mean(X))\n",
    "print 'Variance: {}'.format(variance(X))\n",
    "print 'Standard Deviation: {}'.format(standard_deviation(X))"
   ]
  }
 ],
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