Lessons/Lesson21_Basic_Stats_I_Averages.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic Statistics I:  Averages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An **average** is the central value of a set of numbers. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **arithmetic mean** is the sum of the elements divided by the number of elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Make an array of rank 1\n",
    "arr = np.array([1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's manually calculate the average of array arr."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Manually calculate the average"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, to make our life easier, let's use the built-in method mean to calculate the average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Calculate the average using the built-in method mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate averages on arrays of rank 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Make an array of rank 2\n",
    "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Determine the mean of the array of rank 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Determine the mean of each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Determine the mean of each row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have been practicing on simulated data, so let's now work with a real-work dataset by using the iris dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import the load_iris method \n",
    "from sklearn.datasets import load_iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import pandas, so that we can work with the data frame version of the iris data\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the iris data\n",
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
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       "      <th>petal width (cm)</th>\n",
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       "      <td>5.1</td>\n",
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       "      <td>0.2</td>\n",
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       "      <td>4.9</td>\n",
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       "      <td>4.8</td>\n",
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       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5.7</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.3</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.5</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5.0</td>\n",
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       "      <th>26</th>\n",
       "      <td>5.0</td>\n",
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       "      <th>27</th>\n",
       "      <td>5.2</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>5.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <th>120</th>\n",
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       "      <td>2.0</td>\n",
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       "      <th>122</th>\n",
       "      <td>7.7</td>\n",
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       "      <th>124</th>\n",
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       "      <td>3.3</td>\n",
       "      <td>5.7</td>\n",
       "      <td>2.1</td>\n",
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       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>7.2</td>\n",
       "      <td>3.2</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.8</td>\n",
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       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>6.2</td>\n",
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       "      <td>4.8</td>\n",
       "      <td>1.8</td>\n",
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       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>6.1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.9</td>\n",
       "      <td>1.8</td>\n",
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       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>6.4</td>\n",
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       "      <td>5.6</td>\n",
       "      <td>2.1</td>\n",
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       "      <th>129</th>\n",
       "      <td>7.2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.8</td>\n",
       "      <td>1.6</td>\n",
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       "    <tr>\n",
       "      <th>130</th>\n",
       "      <td>7.4</td>\n",
       "      <td>2.8</td>\n",
       "      <td>6.1</td>\n",
       "      <td>1.9</td>\n",
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       "      <th>131</th>\n",
       "      <td>7.9</td>\n",
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       "      <td>6.4</td>\n",
       "      <td>2.0</td>\n",
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       "    <tr>\n",
       "      <th>132</th>\n",
       "      <td>6.4</td>\n",
       "      <td>2.8</td>\n",
       "      <td>5.6</td>\n",
       "      <td>2.2</td>\n",
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       "    <tr>\n",
       "      <th>133</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.8</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.5</td>\n",
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       "      <th>134</th>\n",
       "      <td>6.1</td>\n",
       "      <td>2.6</td>\n",
       "      <td>5.6</td>\n",
       "      <td>1.4</td>\n",
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       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>7.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.1</td>\n",
       "      <td>2.3</td>\n",
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       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>6.3</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.6</td>\n",
       "      <td>2.4</td>\n",
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       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>6.4</td>\n",
       "      <td>3.1</td>\n",
       "      <td>5.5</td>\n",
       "      <td>1.8</td>\n",
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       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>6.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.8</td>\n",
       "      <td>1.8</td>\n",
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       "      <td>2.1</td>\n",
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       "    <tr>\n",
       "      <th>140</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.1</td>\n",
       "      <td>5.6</td>\n",
       "      <td>2.4</td>\n",
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       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>6.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>5.1</td>\n",
       "      <td>2.3</td>\n",
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       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>5.8</td>\n",
       "      <td>2.7</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.9</td>\n",
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       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>6.8</td>\n",
       "      <td>3.2</td>\n",
       "      <td>5.9</td>\n",
       "      <td>2.3</td>\n",
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       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>6.7</td>\n",
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       "      <td>5.7</td>\n",
       "      <td>2.5</td>\n",
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       "    <tr>\n",
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       "      <td>2.3</td>\n",
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       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
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       "      <td>1.9</td>\n",
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       "      <th>147</th>\n",
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       "      <td>2.0</td>\n",
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       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
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       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
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       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                  5.1               3.5                1.4               0.2\n",
       "1                  4.9               3.0                1.4               0.2\n",
       "2                  4.7               3.2                1.3               0.2\n",
       "3                  4.6               3.1                1.5               0.2\n",
       "4                  5.0               3.6                1.4               0.2\n",
       "5                  5.4               3.9                1.7               0.4\n",
       "6                  4.6               3.4                1.4               0.3\n",
       "7                  5.0               3.4                1.5               0.2\n",
       "8                  4.4               2.9                1.4               0.2\n",
       "9                  4.9               3.1                1.5               0.1\n",
       "10                 5.4               3.7                1.5               0.2\n",
       "11                 4.8               3.4                1.6               0.2\n",
       "12                 4.8               3.0                1.4               0.1\n",
       "13                 4.3               3.0                1.1               0.1\n",
       "14                 5.8               4.0                1.2               0.2\n",
       "15                 5.7               4.4                1.5               0.4\n",
       "16                 5.4               3.9                1.3               0.4\n",
       "17                 5.1               3.5                1.4               0.3\n",
       "18                 5.7               3.8                1.7               0.3\n",
       "19                 5.1               3.8                1.5               0.3\n",
       "20                 5.4               3.4                1.7               0.2\n",
       "21                 5.1               3.7                1.5               0.4\n",
       "22                 4.6               3.6                1.0               0.2\n",
       "23                 5.1               3.3                1.7               0.5\n",
       "24                 4.8               3.4                1.9               0.2\n",
       "25                 5.0               3.0                1.6               0.2\n",
       "26                 5.0               3.4                1.6               0.4\n",
       "27                 5.2               3.5                1.5               0.2\n",
       "28                 5.2               3.4                1.4               0.2\n",
       "29                 4.7               3.2                1.6               0.2\n",
       "..                 ...               ...                ...               ...\n",
       "120                6.9               3.2                5.7               2.3\n",
       "121                5.6               2.8                4.9               2.0\n",
       "122                7.7               2.8                6.7               2.0\n",
       "123                6.3               2.7                4.9               1.8\n",
       "124                6.7               3.3                5.7               2.1\n",
       "125                7.2               3.2                6.0               1.8\n",
       "126                6.2               2.8                4.8               1.8\n",
       "127                6.1               3.0                4.9               1.8\n",
       "128                6.4               2.8                5.6               2.1\n",
       "129                7.2               3.0                5.8               1.6\n",
       "130                7.4               2.8                6.1               1.9\n",
       "131                7.9               3.8                6.4               2.0\n",
       "132                6.4               2.8                5.6               2.2\n",
       "133                6.3               2.8                5.1               1.5\n",
       "134                6.1               2.6                5.6               1.4\n",
       "135                7.7               3.0                6.1               2.3\n",
       "136                6.3               3.4                5.6               2.4\n",
       "137                6.4               3.1                5.5               1.8\n",
       "138                6.0               3.0                4.8               1.8\n",
       "139                6.9               3.1                5.4               2.1\n",
       "140                6.7               3.1                5.6               2.4\n",
       "141                6.9               3.1                5.1               2.3\n",
       "142                5.8               2.7                5.1               1.9\n",
       "143                6.8               3.2                5.9               2.3\n",
       "144                6.7               3.3                5.7               2.5\n",
       "145                6.7               3.0                5.2               2.3\n",
       "146                6.3               2.5                5.0               1.9\n",
       "147                6.5               3.0                5.2               2.0\n",
       "148                6.2               3.4                5.4               2.3\n",
       "149                5.9               3.0                5.1               1.8\n",
       "\n",
       "[150 rows x 4 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert the iris data to a data frame format, so that it's easier to view\n",
    "# and process\n",
    "iris_df = pd.DataFrame(iris['data'], columns = iris['feature_names'])\n",
    "iris_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Determine the mean of each feature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can determine the averages by row, but should we do this? Why or why not?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Determine the mean of each row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How should we interpret a value of averages_row? It's hard to interpret these values, since taking an average across different features does not make sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though we can calculate any statistics that we want, some statistics may not be interpretable. So be careful on your calculations!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great work! You just learned about how to take averages in Python! You learned:\n",
    "\n",
    "- To manually and automatically calculate averages.\n",
    "- To calculate averages by row and by columns. \n",
    "- To calculate averages on a real dataset. \n",
    "- To know when it is appropriate to calculate averages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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