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nilshg/presessionals

Created September 23, 2014 15:49
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presessionals
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"MSc Pre-Sessionals Statistics"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from __future__ import division\n",
"\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"A1. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee = pd.DataFrame({'excess': [0.7,1.9,1.1,2.3,1,0.5,1.4,3,1.3,1.7,0.7,1.3,1.5,2.8,2.7,1.6,1.4,0.2,\n",
" 2.8,2.1,3,1.6,1.6,0.7,2.2,2,1.3,0.9,3.2,2.2,2.2,1.8,1.6,2.3,0.3,1.5,\n",
" 4,0.9,1.1,2.9,0.8,3.1,1.6,1,2.1,1.2,1.7,1.7,1.2,0.6,3.3,1.2,0.9,3.7,\n",
" 1.3,2.2,3.2,2.7,0.4,2,1.8,1.8,3.4,1.3,2.3,2.9,0.6,0.8,3.5,2,1.7,2.5,\n",
" 4.4,2.8,5.7,0.7,3.5,4,3.1,2.7] })"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>excess</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 0.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 1.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 1.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 2.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 1.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
" excess\n",
"0 0.7\n",
"1 1.9\n",
"2 1.1\n",
"3 2.3\n",
"4 1.0"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(a) Arrange the data into an array from lowest to greatest"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.order()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"17 0.2\n",
"34 0.3\n",
"58 0.4\n",
"5 0.5\n",
"49 0.6\n",
"66 0.6\n",
"0 0.7\n",
"75 0.7\n",
"23 0.7\n",
"10 0.7\n",
"67 0.8\n",
"40 0.8\n",
"37 0.9\n",
"52 0.9\n",
"27 0.9\n",
"...\n",
"7 3.0\n",
"20 3.0\n",
"41 3.1\n",
"78 3.1\n",
"56 3.2\n",
"28 3.2\n",
"50 3.3\n",
"62 3.4\n",
"76 3.5\n",
"68 3.5\n",
"53 3.7\n",
"36 4.0\n",
"77 4.0\n",
"72 4.4\n",
"74 5.7\n",
"Name: excess, Length: 80, dtype: float64"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(b) Construct a frequency table with columns for absolute, relative and cumulative frequency"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For absolute frequency, we simply count the data:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"absolute = data_coffee.excess.value_counts()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For relative frequency, we divide the absolute frequency of each unique excess level by the number of total observations:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"relative = data_coffee.excess.value_counts()/len(data_coffee)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For cumulative frequency, we sum up the absolute frequency of each unique excess level:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cumulative = np.cumsum(absolute)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"freq_table = pd.DataFrame({'Absolute': absolute, 'Relative': relative, 'Cumulative': cumulative})"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"freq_table.head(n=8)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Absolute</th>\n",
" <th>Cumulative</th>\n",
" <th>Relative</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1.6</th>\n",
" <td> 5</td>\n",
" <td> 5</td>\n",
" <td> 0.0625</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.3</th>\n",
" <td> 5</td>\n",
" <td> 10</td>\n",
" <td> 0.0625</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.2</th>\n",
" <td> 4</td>\n",
" <td> 14</td>\n",
" <td> 0.0500</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.7</th>\n",
" <td> 4</td>\n",
" <td> 18</td>\n",
" <td> 0.0500</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.7</th>\n",
" <td> 4</td>\n",
" <td> 22</td>\n",
" <td> 0.0500</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.9</th>\n",
" <td> 3</td>\n",
" <td> 25</td>\n",
" <td> 0.0375</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.8</th>\n",
" <td> 3</td>\n",
" <td> 28</td>\n",
" <td> 0.0375</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.3</th>\n",
" <td> 3</td>\n",
" <td> 31</td>\n",
" <td> 0.0375</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
" Absolute Cumulative Relative\n",
"1.6 5 5 0.0625\n",
"1.3 5 10 0.0625\n",
"2.2 4 14 0.0500\n",
"0.7 4 18 0.0500\n",
"1.7 4 22 0.0500\n",
"0.9 3 25 0.0375\n",
"1.8 3 28 0.0375\n",
"2.3 3 31 0.0375"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(c) Construct a histogram for the data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.hist(bins=10);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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CD+5BGJYhNgr75t/bjFtttBncK4lKngl8fMnjfITFoS1JSmQlT07eSx0STgEvBN4zkIqK\nUeUuILEqdwGJVbkLSCryuc6Re2vLV05KUmF8rxIz7hHZN//eZtxqw/cqkaSAHNydVbkLSKzKXUBi\nVe4CkoqcA0furS0HtyQVxozbjHtE9s2/txm32jDjlqSAHNydVbkLSKzKXUBiVe4CkoqcA0furS0H\ntyQVxozbjHtE9s2/txm32jDjlqSAHNydVbkLSKzKXUBiVe4CkoqcA0furS0HtyQVxozbjHtE9s29\n9zrgsVXfdcOGTRw44N/yLknq9+OW1Npj5PihcfBgymMz5WJU0lmVu4DEqtwFJFblLiCxKncByZhx\nO7glqThm3GbcI7LvqO7t+eOl8TxuSQrIwd1ZlbuAxKrcBSRW5S4gsSp3AcmYcTu4Jak4Ztxm3COy\n76jubcZdGjNuSQrIwd1ZlbuAxKrcBSRW5S4gsSp3AcmYcTu4Jak4Ztxm3COy76jubcZdGjNuSQrI\nwd1ZlbuAxKrcBSRW5S4gsSp3AcmYcTu4Jak4Ztxm3COy76jubcZdGjNuSQrIwd1ZlbuAxKrcBSRW\n5S4gsar5PM7Y2FiWj40bN6fprEXGvXHj5nB9L+VfwJFCy/OXdyDvX985eHAfkfs24zbjHpF9R3Xv\nvD3nytfrnLjMvs24JSmglQzu84A7gW8B7xxMOSWpcheQWJW7gMSq3AUkVuUuIBnP4+4+uNcCf0U9\nvE8HXgu8YFBFlWFH7gISs7+yxe1vx464vbXVdXD/DPBtYA74IfBPwKsGVFMh9ucuIDH7K1vc/vbv\nj9tbW10H97OA+5as72+ukyQl1vV0wIE+XTs+voYNG2YYGztukA/b1+OP7+fRR7vee26AlQyjudwF\nJDaXu4DE5nIXkMzc3FzuErLrejrg2cCl1Bk3wCXAE8D7lnzNt4HndK5MkkbTPcBzUzzwePPgk8BT\nqJ8JGbEnJyWpPK8A7qI+sr4kcy2SJEnSaIn84pwrgD3AbbkLSeRU4IvA7cA3gbfmLWegngrcSB3t\n7QTek7ecZNYC24HrcxeSwBxwK3V/N+UtJYkJ4KPAHdTfo2ev1sZrqeOTSWAd8fLvnwPOJO7gPgmY\nai6vp47DIv37Hd98Hge+Brw0Yy2pvB34CPDJ3IUkcC+Q/u338rkKeENzeRw44UhflOK9SqK/OOcG\nYF/uIhJ6gMWX3T1C/ZP/5HzlDNz3m89PoT7I2JuxlhROAc4HLiPtm8jlFLWvE6gPDK9o1o8BDx/p\nC1MMbl+cE8ck9W8XN2auY5DWUP9g2kMdCe3MW87AfRB4B/XpuRHNA18AbgbelLmWQTsNeAi4EvhP\n4MMs/oZ4mBSD27+TFMN66qztbdRH3lE8QR0FnQL8PDCdtZrBeiXwIHX+G/Wo9Bzqg4lXAG+hPkKN\nYhz4KeCvm8+PAhcf6QtTDO7/oX6Ca8Gp1EfdKsc64DrgH4BPZK4llYeBf6V+Q/YoXgJcQJ0DXwO8\nDLg6a0WDt7v5/BDwcepoNor7m4+vN+uPUg/wVTEKL86ZJO6Tk2PU/7N/MHchCTyd+ll7gOOALwG/\nmK+cpM4l3lklxwMbmstPA74CvDxfOUl8CXhec/lSDn81enKRX5xzDbAL+D/qLP/CvOUM3Eup44Qd\n1L9yb2fxrQ1KdwZ1driD+pSyd+QtJ6lziXdWyWnU/3Y7qE9VjTZbAH6S+oj7FuBjLHNWiSRJkiRJ\nkiRJkiRJkiRJkiRJkqSj+H/4tFgK0BwB9QAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0xc5f3fd0>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(d) Calculate the range and inter-quartile range"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"range_coffee = data_coffee.excess.max() - data_coffee.excess.min()\n",
"print \"The range of the data is %.2f\\n\" % range_coffee"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The range of the data is 5.50\n",
"\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"int_q_range = data_coffee.excess.quantile(q = 0.75)- data_coffee.excess.quantile(q = 0.25)\n",
"print \"The inter quartile range is %.2f\" % int_q_range"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The inter quartile range is 1.53\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(e) Calculate the mean and standard deviation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.mean()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 18,
"text": [
"1.9587499999999998"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.std()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"1.067315780209187"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(f) Calculate the median and the mode, comment on symmetry of distribution"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.median()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 20,
"text": [
"1.75"
]
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.mode()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 21,
"text": [
"0 1.3\n",
"1 1.6\n",
"dtype: float64"
]
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(figsize = (9, 7))\n",
"plt.bar(np.arange(0, 80), data_coffee.excess.order())\n",
"plt.suptitle('Cumulative Distribution Function', fontsize = 16);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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AACAYwgQAALBCmAAQcVxoC4gtXOgLQMQFvwAXgGjDkQkAAGCFMAEAAKwQJgAA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\nAFb+H9uvUh/lDd+LAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0xd2332e8>"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(g) Calculate the skewness and kurtosis"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.skew()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 24,
"text": [
"0.77756435303347637"
]
}
],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_coffee.excess.kurtosis()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 25,
"text": [
"0.73131914545024934"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"A2 - 40 Observations Day, 40 Observations Night"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_day = data_coffee.iloc[0:40]\n",
"data_night = data_coffee.iloc[40:80]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(a) Construct a frequency table to compare the two groups"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"absolute_day = data_day.excess.value_counts()\n",
"relative_day = absolute_day/len(data_day)\n",
"cumulative_day = np.cumsum(absolute_day)\n",
"absolute_night = data_night.excess.value_counts()\n",
"relative_night = absolute_night/len(data_night)\n",
"cumulative_night = np.cumsum(absolute_night)\n",
"\n",
"freq_table_2 = pd.DataFrame( {'Day: Absolute': absolute_day, 'Day: Relative': relative_day,\n",
" 'Day: Cumulative': cumulative_day, 'Night: Absolute': absolute_night,\n",
" 'Night: Relative': relative_night, 'Night: Cumulative': cumulative_night} )\n",
"\n",
"freq_table_2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Day: Absolute</th>\n",
" <th>Day: Cumulative</th>\n",
" <th>Day: Relative</th>\n",
" <th>Night: Absolute</th>\n",
" <th>Night: Cumulative</th>\n",
" <th>Night: Relative</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0.2</th>\n",
" <td> 1</td>\n",
" <td> 39</td>\n",
" <td> 0.025</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.3</th>\n",
" <td> 1</td>\n",
" <td> 28</td>\n",
" <td> 0.025</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.4</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 34</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.5</th>\n",
" <td> 1</td>\n",
" <td> 40</td>\n",
" <td> 0.025</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.6</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 2</td>\n",
" <td> 20</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.7</th>\n",
" <td> 3</td>\n",
" <td> 7</td>\n",
" <td> 0.075</td>\n",
" <td> 1</td>\n",
" <td> 26</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.8</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 2</td>\n",
" <td> 22</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0.9</th>\n",
" <td> 2</td>\n",
" <td> 19</td>\n",
" <td> 0.050</td>\n",
" <td> 1</td>\n",
" <td> 39</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.0</th>\n",
" <td> 1</td>\n",
" <td> 30</td>\n",
" <td> 0.025</td>\n",
" <td> 1</td>\n",
" <td> 23</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.1</th>\n",
" <td> 2</td>\n",
" <td> 25</td>\n",
" <td> 0.050</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.2</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 3</td>\n",
" <td> 6</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.3</th>\n",
" <td> 3</td>\n",
" <td> 10</td>\n",
" <td> 0.075</td>\n",
" <td> 2</td>\n",
" <td> 12</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.4</th>\n",
" <td> 2</td>\n",
" <td> 21</td>\n",
" <td> 0.050</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.5</th>\n",
" <td> 2</td>\n",
" <td> 15</td>\n",
" <td> 0.050</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.6</th>\n",
" <td> 4</td>\n",
" <td> 4</td>\n",
" <td> 0.100</td>\n",
" <td> 1</td>\n",
" <td> 35</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.7</th>\n",
" <td> 1</td>\n",
" <td> 34</td>\n",
" <td> 0.025</td>\n",
" <td> 3</td>\n",
" <td> 3</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.8</th>\n",
" <td> 1</td>\n",
" <td> 32</td>\n",
" <td> 0.025</td>\n",
" <td> 2</td>\n",
" <td> 14</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1.9</th>\n",
" <td> 1</td>\n",
" <td> 38</td>\n",
" <td> 0.025</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.0</th>\n",
" <td> 1</td>\n",
" <td> 31</td>\n",
" <td> 0.025</td>\n",
" <td> 2</td>\n",
" <td> 18</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.1</th>\n",
" <td> 1</td>\n",
" <td> 37</td>\n",
" <td> 0.025</td>\n",
" <td> 1</td>\n",
" <td> 38</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.2</th>\n",
" <td> 3</td>\n",
" <td> 13</td>\n",
" <td> 0.075</td>\n",
" <td> 1</td>\n",
" <td> 33</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.3</th>\n",
" <td> 2</td>\n",
" <td> 27</td>\n",
" <td> 0.050</td>\n",
" <td> 1</td>\n",
" <td> 40</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.5</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 24</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.7</th>\n",
" <td> 1</td>\n",
" <td> 35</td>\n",
" <td> 0.025</td>\n",
" <td> 2</td>\n",
" <td> 10</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.8</th>\n",
" <td> 2</td>\n",
" <td> 23</td>\n",
" <td> 0.050</td>\n",
" <td> 1</td>\n",
" <td> 28</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2.9</th>\n",
" <td> 1</td>\n",
" <td> 33</td>\n",
" <td> 0.025</td>\n",
" <td> 1</td>\n",
" <td> 32</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.0</th>\n",
" <td> 2</td>\n",
" <td> 17</td>\n",
" <td> 0.050</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.1</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 2</td>\n",
" <td> 16</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.2</th>\n",
" <td> 1</td>\n",
" <td> 36</td>\n",
" <td> 0.025</td>\n",
" <td> 1</td>\n",
" <td> 31</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.3</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 30</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.4</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 29</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.5</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 2</td>\n",
" <td> 8</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.7</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 36</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.0</th>\n",
" <td> 1</td>\n",
" <td> 29</td>\n",
" <td> 0.025</td>\n",
" <td> 1</td>\n",
" <td> 25</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.4</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 27</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5.7</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td> NaN</td>\n",
" <td> 1</td>\n",
" <td> 37</td>\n",
" <td> 0.025</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>36 rows \u00d7 6 columns</p>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 28,
"text": [
" Day: Absolute Day: Cumulative Day: Relative Night: Absolute \\\n",
"0.2 1 39 0.025 NaN \n",
"0.3 1 28 0.025 NaN \n",
"0.4 NaN NaN NaN 1 \n",
"0.5 1 40 0.025 NaN \n",
"0.6 NaN NaN NaN 2 \n",
"0.7 3 7 0.075 1 \n",
"0.8 NaN NaN NaN 2 \n",
"0.9 2 19 0.050 1 \n",
"1.0 1 30 0.025 1 \n",
"1.1 2 25 0.050 NaN \n",
"1.2 NaN NaN NaN 3 \n",
"1.3 3 10 0.075 2 \n",
"1.4 2 21 0.050 NaN \n",
"1.5 2 15 0.050 NaN \n",
"1.6 4 4 0.100 1 \n",
"1.7 1 34 0.025 3 \n",
"1.8 1 32 0.025 2 \n",
"1.9 1 38 0.025 NaN \n",
"2.0 1 31 0.025 2 \n",
"2.1 1 37 0.025 1 \n",
"2.2 3 13 0.075 1 \n",
"2.3 2 27 0.050 1 \n",
"2.5 NaN NaN NaN 1 \n",
"2.7 1 35 0.025 2 \n",
"2.8 2 23 0.050 1 \n",
"2.9 1 33 0.025 1 \n",
"3.0 2 17 0.050 NaN \n",
"3.1 NaN NaN NaN 2 \n",
"3.2 1 36 0.025 1 \n",
"3.3 NaN NaN NaN 1 \n",
"3.4 NaN NaN NaN 1 \n",
"3.5 NaN NaN NaN 2 \n",
"3.7 NaN NaN NaN 1 \n",
"4.0 1 29 0.025 1 \n",
"4.4 NaN NaN NaN 1 \n",
"5.7 NaN NaN NaN 1 \n",
"\n",
" Night: Cumulative Night: Relative \n",
"0.2 NaN NaN \n",
"0.3 NaN NaN \n",
"0.4 34 0.025 \n",
"0.5 NaN NaN \n",
"0.6 20 0.050 \n",
"0.7 26 0.025 \n",
"0.8 22 0.050 \n",
"0.9 39 0.025 \n",
"1.0 23 0.025 \n",
"1.1 NaN NaN \n",
"1.2 6 0.075 \n",
"1.3 12 0.050 \n",
"1.4 NaN NaN \n",
"1.5 NaN NaN \n",
"1.6 35 0.025 \n",
"1.7 3 0.075 \n",
"1.8 14 0.050 \n",
"1.9 NaN NaN \n",
"2.0 18 0.050 \n",
"2.1 38 0.025 \n",
"2.2 33 0.025 \n",
"2.3 40 0.025 \n",
"2.5 24 0.025 \n",
"2.7 10 0.050 \n",
"2.8 28 0.025 \n",
"2.9 32 0.025 \n",
"3.0 NaN NaN \n",
"3.1 16 0.050 \n",
"3.2 31 0.025 \n",
"3.3 30 0.025 \n",
"3.4 29 0.025 \n",
"3.5 8 0.050 \n",
"3.7 36 0.025 \n",
"4.0 25 0.025 \n",
"4.4 27 0.025 \n",
"5.7 37 0.025 \n",
"\n",
"[36 rows x 6 columns]"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(b) Compare the two groups using a frequency polygon"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"bins = np.linspace(data_coffee.excess.min(), data_coffee.excess.max(), 15)\n",
"night_hist, bins = np.histogram(data_night.excess, bins = bins)\n",
"day_hist, bins = np.histogram(data_day.excess, bins = bins)\n",
"center = (bins[:-1] + bins[1:]) / 2\n",
"\n",
"fig, ax = plt.subplots(figsize = (9,7))\n",
"ax.bar(center, night_hist, align='center', width=0.1, color = 'cornflowerblue', label='Night')\n",
"ax.bar(center+0.1, day_hist, align='center', width=0.1, color = 'blanchedalmond', label='Day')\n",
"ax.set_xlabel('Value')\n",
"ax.set_ylabel('Frequency')\n",
"ax.legend(loc=0)\n",
"fig.suptitle('Histogram by Time of Day', fontsize=14);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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0cbQoAABQcXkNHydPnlRISIjneWhoqAoKChwtCgAAVFxew0f16tWVlfXryW6Z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\nRK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0xd1a6898>"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(c) Calculate mean and standard deviation in each group"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print 'Mean during the day is %.2f, the standard deviation is %.2f' % (data_day.excess.mean(), data_day.excess.std())\n",
"print 'Mean during the night is %.2f, the standard deviation is %.2f' % (data_night.excess.mean(), data_night.excess.std())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mean during the day is 1.73, the standard deviation is 0.87\n",
"Mean during the night is 2.18, the standard deviation is 1.20\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"A3. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_grades = pd.DataFrame( {'grade': [87,77,67,67,47,60,77,67,57,77,\n",
" 73,75,63,97,75,77,80,80,77,63,\n",
" 87,93,63,60,75,20,97,90,73,33,\n",
" 60,67,90,60,42,67,67,57,73,80]} )"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(a) Arrange the data from lowest to highest"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data_grades.grade.order()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"25 20\n",
"29 33\n",
"34 42\n",
"4 47\n",
"8 57\n",
"37 57\n",
"30 60\n",
"23 60\n",
"5 60\n",
"33 60\n",
"22 63\n",
"12 63\n",
"19 63\n",
"7 67\n",
"31 67\n",
"2 67\n",
"36 67\n",
"35 67\n",
"3 67\n",
"10 73\n",
"28 73\n",
"38 73\n",
"11 75\n",
"24 75\n",
"14 75\n",
"9 77\n",
"6 77\n",
"18 77\n",
"15 77\n",
"1 77\n",
"39 80\n",
"17 80\n",
"16 80\n",
"20 87\n",
"0 87\n",
"32 90\n",
"27 90\n",
"21 93\n",
"26 97\n",
"13 97\n",
"Name: grade, dtype: int64"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"absolute = data_grades.grade.value_counts()\n",
"relative = data_grades.grade.value_counts()/len(data_grades)\n",
"cumulative = np.cumsum(absolute)\n",
"freq_table = pd.DataFrame({'Absolute': absolute, 'Relative': relative, 'Cumulative': cumulative})\n",
"freq_table.head(n=8)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Absolute</th>\n",
" <th>Cumulative</th>\n",
" <th>Relative</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>67</th>\n",
" <td> 6</td>\n",
" <td> 6</td>\n",
" <td> 0.150</td>\n",
" </tr>\n",
" <tr>\n",
" <th>77</th>\n",
" <td> 5</td>\n",
" <td> 11</td>\n",
" <td> 0.125</td>\n",
" </tr>\n",
" <tr>\n",
" <th>60</th>\n",
" <td> 4</td>\n",
" <td> 15</td>\n",
" <td> 0.100</td>\n",
" </tr>\n",
" <tr>\n",
" <th>63</th>\n",
" <td> 3</td>\n",
" <td> 18</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>80</th>\n",
" <td> 3</td>\n",
" <td> 21</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75</th>\n",
" <td> 3</td>\n",
" <td> 24</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>73</th>\n",
" <td> 3</td>\n",
" <td> 27</td>\n",
" <td> 0.075</td>\n",
" </tr>\n",
" <tr>\n",
" <th>57</th>\n",
" <td> 2</td>\n",
" <td> 29</td>\n",
" <td> 0.050</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 21,
"text": [
" Absolute Cumulative Relative\n",
"67 6 6 0.150\n",
"77 5 11 0.125\n",
"60 4 15 0.100\n",
"63 3 18 0.075\n",
"80 3 21 0.075\n",
"75 3 24 0.075\n",
"73 3 27 0.075\n",
"57 2 29 0.050"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(c) Construct a histogram"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.hist(data_grades.grade);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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SJEmSJEmSJEmSJEmSpMXh/wFoiQJv4CvKAgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x403dac8>"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(d) Range and Interquartile Range"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"range_grades = data_grades.grade.max() - data_grades.grade.min()\n",
"int_q_range_grades = data_grades.grade.quantile(q=0.75) - data_grades.grade.quantile(q=0.25)\n",
"print \"The range of the data is %.1f\" % range_grades\n",
"print \"The interquartile range is %.1f\" % int_q_range_grades"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The range of the data is 77.0\n",
"The interquartile range is 15.5\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(e) Mean and Standard Deviation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"The mean of the data is %.2f, the standard deviation is %.2f\" %(data_grades.grade.mean(), data_grades.grade.std())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mean of the data is 69.92, the standard deviation is 16.12\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(f) Median and Mode"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"The median is %.1f, the mode is %.1f\" % (data_grades.grade.median(), data_grades.grade.mode())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The median is 73.0, the mode is 67.0\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"(g) Skewness and Kurtosis"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"The skewness is %.2f, the kurtosis is %.2f\" % (data_grades.grade.skew(), data_grades.grade.kurt())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The skewness is -0.87, the kurtosis is 1.61\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"B3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing a student with a grade between 50 and 59 at random:\n",
"\n",
"We count the number of students with a grade below sixty and above 49 and divide by the total number of students:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"len(data_grades[(data_grades.grade < 60) & (data_grades.grade > 49)])/len(data_grades)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 29,
"text": [
"0.05"
]
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing a student with a grade between 70 and 99 at random:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"len(data_grades[(data_grades.grade < 99) & (data_grades.grade >= 70)])/len(data_grades)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 48,
"text": [
"0.525"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"B4."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing a jar with excess weight between 0 and 1.99g:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"len(data_coffee[data_coffee.excess < 2])/len(data_coffee)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 49,
"text": [
"0.55"
]
}
],
"prompt_number": 49
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing a jar with excess weight between 4 and 5.99g:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"len(data_coffee[(data_coffee.excess >= 4) & (data_coffee.excess < 6)])/len(data_coffee)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 50,
"text": [
"0.05"
]
}
],
"prompt_number": 50
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing two jars at random between 0 and 0.99g with replacement:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"below_one = len(data_coffee[data_coffee.excess < 1])\n",
"total_jars = len(data_coffee)\n",
"\n",
"prob = (below_one / total_jars) * (below_one / total_jars)\n",
"\n",
"print 'Probability with replacement is %.3f' % prob"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability with replacement is 0.035\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Probability of drawing two jars at random between 0 and 0.99g without replacement:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"prob = (below_one / total_jars) * ( (below_one-1) / (total_jars-1) )\n",
"print 'Probability without replacement is %.3f' % prob"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Probability without replacement is 0.033\n"
]
}
],
"prompt_number": 24
}
],
"metadata": {}
}
]
}
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