P30. Unsupervised ML - K-Means Clustering (Non-Hierarchical Clustering) (Univ.)-ver-01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised ML - K-Means Clustering \n",
    "# (Non-Hierarchical Clustering) (Univ.)\n",
    "# Using sklearn normalize function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.preprocessing import normalize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Univ</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brown</td>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CalTech</td>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>CMU</td>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Columbia</td>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cornell</td>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Dartmouth</td>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duke</td>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Georgetown</td>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Harvard</td>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>JohnsHopkins</td>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>MIT</td>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Northwestern</td>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NotreDame</td>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>PennState</td>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Princeton</td>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Purdue</td>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Stanford</td>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>TexasA&amp;M</td>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>UCBerkeley</td>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>UChicago</td>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>UMichigan</td>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>UPenn</td>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>UVA</td>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>UWisconsin</td>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Yale</td>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "            Univ   SAT  Top10  Accept  SFRatio  Expenses  GradRate\n",
       "0          Brown  1310     89      22       13     22704        94\n",
       "1        CalTech  1415    100      25        6     63575        81\n",
       "2            CMU  1260     62      59        9     25026        72\n",
       "3       Columbia  1310     76      24       12     31510        88\n",
       "4        Cornell  1280     83      33       13     21864        90\n",
       "5      Dartmouth  1340     89      23       10     32162        95\n",
       "6           Duke  1315     90      30       12     31585        95\n",
       "7     Georgetown  1255     74      24       12     20126        92\n",
       "8        Harvard  1400     91      14       11     39525        97\n",
       "9   JohnsHopkins  1305     75      44        7     58691        87\n",
       "10           MIT  1380     94      30       10     34870        91\n",
       "11  Northwestern  1260     85      39       11     28052        89\n",
       "12     NotreDame  1255     81      42       13     15122        94\n",
       "13     PennState  1081     38      54       18     10185        80\n",
       "14     Princeton  1375     91      14        8     30220        95\n",
       "15        Purdue  1005     28      90       19      9066        69\n",
       "16      Stanford  1360     90      20       12     36450        93\n",
       "17      TexasA&M  1075     49      67       25      8704        67\n",
       "18    UCBerkeley  1240     95      40       17     15140        78\n",
       "19      UChicago  1290     75      50       13     38380        87\n",
       "20     UMichigan  1180     65      68       16     15470        85\n",
       "21         UPenn  1285     80      36       11     27553        90\n",
       "22           UVA  1225     77      44       14     13349        92\n",
       "23    UWisconsin  1085     40      69       15     11857        71\n",
       "24          Yale  1375     95      19       11     43514        96"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import dataset\n",
    "univ=pd.read_csv('Database/Universities.csv')\n",
    "univ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT  Top10  Accept  SFRatio  Expenses  GradRate\n",
       "0   1310     89      22       13     22704        94\n",
       "1   1415    100      25        6     63575        81\n",
       "2   1260     62      59        9     25026        72\n",
       "3   1310     76      24       12     31510        88\n",
       "4   1280     83      33       13     21864        90\n",
       "5   1340     89      23       10     32162        95\n",
       "6   1315     90      30       12     31585        95\n",
       "7   1255     74      24       12     20126        92\n",
       "8   1400     91      14       11     39525        97\n",
       "9   1305     75      44        7     58691        87\n",
       "10  1380     94      30       10     34870        91\n",
       "11  1260     85      39       11     28052        89\n",
       "12  1255     81      42       13     15122        94\n",
       "13  1081     38      54       18     10185        80\n",
       "14  1375     91      14        8     30220        95\n",
       "15  1005     28      90       19      9066        69\n",
       "16  1360     90      20       12     36450        93\n",
       "17  1075     49      67       25      8704        67\n",
       "18  1240     95      40       17     15140        78\n",
       "19  1290     75      50       13     38380        87\n",
       "20  1180     65      68       16     15470        85\n",
       "21  1285     80      36       11     27553        90\n",
       "22  1225     77      44       14     13349        92\n",
       "23  1085     40      69       15     11857        71\n",
       "24  1375     95      19       11     43514        96"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "univ2=univ.iloc[:,1:]\n",
    "univ2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.057602</td>\n",
       "      <td>0.003913</td>\n",
       "      <td>0.000967</td>\n",
       "      <td>0.000572</td>\n",
       "      <td>0.998323</td>\n",
       "      <td>0.004133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.022252</td>\n",
       "      <td>0.001573</td>\n",
       "      <td>0.000393</td>\n",
       "      <td>0.000094</td>\n",
       "      <td>0.999750</td>\n",
       "      <td>0.001274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.050283</td>\n",
       "      <td>0.002474</td>\n",
       "      <td>0.002355</td>\n",
       "      <td>0.000359</td>\n",
       "      <td>0.998725</td>\n",
       "      <td>0.002873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.041538</td>\n",
       "      <td>0.002410</td>\n",
       "      <td>0.000761</td>\n",
       "      <td>0.000381</td>\n",
       "      <td>0.999130</td>\n",
       "      <td>0.002790</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.058443</td>\n",
       "      <td>0.003790</td>\n",
       "      <td>0.001507</td>\n",
       "      <td>0.000594</td>\n",
       "      <td>0.998274</td>\n",
       "      <td>0.004109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.041628</td>\n",
       "      <td>0.002765</td>\n",
       "      <td>0.000715</td>\n",
       "      <td>0.000311</td>\n",
       "      <td>0.999125</td>\n",
       "      <td>0.002951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.041597</td>\n",
       "      <td>0.002847</td>\n",
       "      <td>0.000949</td>\n",
       "      <td>0.000380</td>\n",
       "      <td>0.999125</td>\n",
       "      <td>0.003005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.062235</td>\n",
       "      <td>0.003670</td>\n",
       "      <td>0.001190</td>\n",
       "      <td>0.000595</td>\n",
       "      <td>0.998043</td>\n",
       "      <td>0.004562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.035398</td>\n",
       "      <td>0.002301</td>\n",
       "      <td>0.000354</td>\n",
       "      <td>0.000278</td>\n",
       "      <td>0.999368</td>\n",
       "      <td>0.002453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.022230</td>\n",
       "      <td>0.001278</td>\n",
       "      <td>0.000750</td>\n",
       "      <td>0.000119</td>\n",
       "      <td>0.999751</td>\n",
       "      <td>0.001482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.039544</td>\n",
       "      <td>0.002694</td>\n",
       "      <td>0.000860</td>\n",
       "      <td>0.000287</td>\n",
       "      <td>0.999210</td>\n",
       "      <td>0.002608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.044871</td>\n",
       "      <td>0.003027</td>\n",
       "      <td>0.001389</td>\n",
       "      <td>0.000392</td>\n",
       "      <td>0.998982</td>\n",
       "      <td>0.003169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.082704</td>\n",
       "      <td>0.005338</td>\n",
       "      <td>0.002768</td>\n",
       "      <td>0.000857</td>\n",
       "      <td>0.996536</td>\n",
       "      <td>0.006195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.105538</td>\n",
       "      <td>0.003710</td>\n",
       "      <td>0.005272</td>\n",
       "      <td>0.001757</td>\n",
       "      <td>0.994362</td>\n",
       "      <td>0.007810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.045452</td>\n",
       "      <td>0.003008</td>\n",
       "      <td>0.000463</td>\n",
       "      <td>0.000264</td>\n",
       "      <td>0.998957</td>\n",
       "      <td>0.003140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.110170</td>\n",
       "      <td>0.003069</td>\n",
       "      <td>0.009866</td>\n",
       "      <td>0.002083</td>\n",
       "      <td>0.993828</td>\n",
       "      <td>0.007564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.037285</td>\n",
       "      <td>0.002467</td>\n",
       "      <td>0.000548</td>\n",
       "      <td>0.000329</td>\n",
       "      <td>0.999298</td>\n",
       "      <td>0.002550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.122566</td>\n",
       "      <td>0.005587</td>\n",
       "      <td>0.007639</td>\n",
       "      <td>0.002850</td>\n",
       "      <td>0.992382</td>\n",
       "      <td>0.007639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.081626</td>\n",
       "      <td>0.006254</td>\n",
       "      <td>0.002633</td>\n",
       "      <td>0.001119</td>\n",
       "      <td>0.996626</td>\n",
       "      <td>0.005135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.033592</td>\n",
       "      <td>0.001953</td>\n",
       "      <td>0.001302</td>\n",
       "      <td>0.000339</td>\n",
       "      <td>0.999430</td>\n",
       "      <td>0.002266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.076053</td>\n",
       "      <td>0.004189</td>\n",
       "      <td>0.004383</td>\n",
       "      <td>0.001031</td>\n",
       "      <td>0.997070</td>\n",
       "      <td>0.005478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.046586</td>\n",
       "      <td>0.002900</td>\n",
       "      <td>0.001305</td>\n",
       "      <td>0.000399</td>\n",
       "      <td>0.998904</td>\n",
       "      <td>0.003263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.091379</td>\n",
       "      <td>0.005744</td>\n",
       "      <td>0.003282</td>\n",
       "      <td>0.001044</td>\n",
       "      <td>0.995770</td>\n",
       "      <td>0.006863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.091123</td>\n",
       "      <td>0.003359</td>\n",
       "      <td>0.005795</td>\n",
       "      <td>0.001260</td>\n",
       "      <td>0.995798</td>\n",
       "      <td>0.005963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.031583</td>\n",
       "      <td>0.002182</td>\n",
       "      <td>0.000436</td>\n",
       "      <td>0.000253</td>\n",
       "      <td>0.999496</td>\n",
       "      <td>0.002205</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         SAT     Top10    Accept   SFRatio  Expenses  GradRate\n",
       "0   0.057602  0.003913  0.000967  0.000572  0.998323  0.004133\n",
       "1   0.022252  0.001573  0.000393  0.000094  0.999750  0.001274\n",
       "2   0.050283  0.002474  0.002355  0.000359  0.998725  0.002873\n",
       "3   0.041538  0.002410  0.000761  0.000381  0.999130  0.002790\n",
       "4   0.058443  0.003790  0.001507  0.000594  0.998274  0.004109\n",
       "5   0.041628  0.002765  0.000715  0.000311  0.999125  0.002951\n",
       "6   0.041597  0.002847  0.000949  0.000380  0.999125  0.003005\n",
       "7   0.062235  0.003670  0.001190  0.000595  0.998043  0.004562\n",
       "8   0.035398  0.002301  0.000354  0.000278  0.999368  0.002453\n",
       "9   0.022230  0.001278  0.000750  0.000119  0.999751  0.001482\n",
       "10  0.039544  0.002694  0.000860  0.000287  0.999210  0.002608\n",
       "11  0.044871  0.003027  0.001389  0.000392  0.998982  0.003169\n",
       "12  0.082704  0.005338  0.002768  0.000857  0.996536  0.006195\n",
       "13  0.105538  0.003710  0.005272  0.001757  0.994362  0.007810\n",
       "14  0.045452  0.003008  0.000463  0.000264  0.998957  0.003140\n",
       "15  0.110170  0.003069  0.009866  0.002083  0.993828  0.007564\n",
       "16  0.037285  0.002467  0.000548  0.000329  0.999298  0.002550\n",
       "17  0.122566  0.005587  0.007639  0.002850  0.992382  0.007639\n",
       "18  0.081626  0.006254  0.002633  0.001119  0.996626  0.005135\n",
       "19  0.033592  0.001953  0.001302  0.000339  0.999430  0.002266\n",
       "20  0.076053  0.004189  0.004383  0.001031  0.997070  0.005478\n",
       "21  0.046586  0.002900  0.001305  0.000399  0.998904  0.003263\n",
       "22  0.091379  0.005744  0.003282  0.001044  0.995770  0.006863\n",
       "23  0.091123  0.003359  0.005795  0.001260  0.995798  0.005963\n",
       "24  0.031583  0.002182  0.000436  0.000253  0.999496  0.002205"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Normalize heterogenous numerical data using standard scalar fit transform to dataset\n",
    "univ_norm=pd.DataFrame(normalize(univ2),columns=univ2.columns)\n",
    "univ_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Elbow Graph to find optimum number of  clusters (K value) from K values range\n",
    "# The K-means algorithm aims to choose centroids that minimise the inertia, or within-cluster sum-of-squares criterion WCSS \n",
    "# random state can be anything from 0 to 42, but the same number to be used everytime,so that the results don't change. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# within-cluster sum-of-squares criterion \n",
    "wcss=[]\n",
    "for i in range(1,11):\n",
    "    kmeans=KMeans(n_clusters=i,random_state=1)  \n",
    "    kmeans.fit(univ_norm)\n",
    "    wcss.append(kmeans.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "# Plot K values range vs WCSS to get Elbow graph for choosing K (no. of clusters)\n",
    "plt.plot(range(1,11),wcss)\n",
    "plt.title('Elbow Graph')\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('WCSS')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build Cluster algorithm using K=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=4, random_state=42)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cluster algorithm using K=4\n",
    "clusters4=KMeans(4,random_state=42).fit(univ_norm)\n",
    "clusters4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 3, 0, 3, 2, 3, 1, 2, 1, 0,\n",
       "       1, 1, 2])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusters4.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Univ</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "      <th>clusters4id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brown</td>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CalTech</td>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>CMU</td>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Columbia</td>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cornell</td>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Dartmouth</td>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duke</td>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Georgetown</td>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Harvard</td>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>JohnsHopkins</td>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>MIT</td>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Northwestern</td>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NotreDame</td>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>PennState</td>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Princeton</td>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Purdue</td>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Stanford</td>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>TexasA&amp;M</td>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>UCBerkeley</td>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>UChicago</td>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>UMichigan</td>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>UPenn</td>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>UVA</td>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>UWisconsin</td>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Yale</td>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Univ   SAT  Top10  Accept  SFRatio  Expenses  GradRate  \\\n",
       "0          Brown  1310     89      22       13     22704        94   \n",
       "1        CalTech  1415    100      25        6     63575        81   \n",
       "2            CMU  1260     62      59        9     25026        72   \n",
       "3       Columbia  1310     76      24       12     31510        88   \n",
       "4        Cornell  1280     83      33       13     21864        90   \n",
       "5      Dartmouth  1340     89      23       10     32162        95   \n",
       "6           Duke  1315     90      30       12     31585        95   \n",
       "7     Georgetown  1255     74      24       12     20126        92   \n",
       "8        Harvard  1400     91      14       11     39525        97   \n",
       "9   JohnsHopkins  1305     75      44        7     58691        87   \n",
       "10           MIT  1380     94      30       10     34870        91   \n",
       "11  Northwestern  1260     85      39       11     28052        89   \n",
       "12     NotreDame  1255     81      42       13     15122        94   \n",
       "13     PennState  1081     38      54       18     10185        80   \n",
       "14     Princeton  1375     91      14        8     30220        95   \n",
       "15        Purdue  1005     28      90       19      9066        69   \n",
       "16      Stanford  1360     90      20       12     36450        93   \n",
       "17      TexasA&M  1075     49      67       25      8704        67   \n",
       "18    UCBerkeley  1240     95      40       17     15140        78   \n",
       "19      UChicago  1290     75      50       13     38380        87   \n",
       "20     UMichigan  1180     65      68       16     15470        85   \n",
       "21         UPenn  1285     80      36       11     27553        90   \n",
       "22           UVA  1225     77      44       14     13349        92   \n",
       "23    UWisconsin  1085     40      69       15     11857        71   \n",
       "24          Yale  1375     95      19       11     43514        96   \n",
       "\n",
       "    clusters4id  \n",
       "0             0  \n",
       "1             2  \n",
       "2             0  \n",
       "3             0  \n",
       "4             0  \n",
       "5             0  \n",
       "6             0  \n",
       "7             0  \n",
       "8             2  \n",
       "9             2  \n",
       "10            0  \n",
       "11            0  \n",
       "12            1  \n",
       "13            3  \n",
       "14            0  \n",
       "15            3  \n",
       "16            2  \n",
       "17            3  \n",
       "18            1  \n",
       "19            2  \n",
       "20            1  \n",
       "21            0  \n",
       "22            1  \n",
       "23            1  \n",
       "24            2  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assign clusters to the data set\n",
    "univ4=univ.copy()\n",
    "univ4['clusters4id']=clusters4.labels_\n",
    "univ4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.81618202e-02, 3.04523863e-03, 1.13270229e-03, 4.11972955e-04,\n",
       "        9.98799819e-01, 3.32773470e-03],\n",
       "       [8.45769889e-02, 4.97680644e-03, 3.77213808e-03, 1.06221659e-03,\n",
       "        9.96360145e-01, 5.92662638e-03],\n",
       "       [3.03899663e-02, 1.95892248e-03, 6.30562482e-04, 2.35316328e-04,\n",
       "        9.99515514e-01, 2.03809454e-03],\n",
       "       [1.12757732e-01, 4.12201708e-03, 7.59230756e-03, 2.23017002e-03,\n",
       "        9.93524025e-01, 7.67108453e-03]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the centroids for K=4 clusters with 6 variables\n",
    "clusters4.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>clusters4id</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1306.363636</td>\n",
       "      <td>83.000000</td>\n",
       "      <td>30.363636</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>27788.363636</td>\n",
       "      <td>90.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1197.000000</td>\n",
       "      <td>71.600000</td>\n",
       "      <td>52.600000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>14187.600000</td>\n",
       "      <td>84.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1357.500000</td>\n",
       "      <td>87.666667</td>\n",
       "      <td>28.666667</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>46689.166667</td>\n",
       "      <td>90.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1053.666667</td>\n",
       "      <td>38.333333</td>\n",
       "      <td>70.333333</td>\n",
       "      <td>20.666667</td>\n",
       "      <td>9318.333333</td>\n",
       "      <td>72.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  clusters4id          SAT      Top10     Accept    SFRatio      Expenses  \\\n",
       "                      mean       mean       mean       mean          mean   \n",
       "0           0  1306.363636  83.000000  30.363636  11.000000  27788.363636   \n",
       "1           1  1197.000000  71.600000  52.600000  15.000000  14187.600000   \n",
       "2           2  1357.500000  87.666667  28.666667  10.000000  46689.166667   \n",
       "3           3  1053.666667  38.333333  70.333333  20.666667   9318.333333   \n",
       "\n",
       "    GradRate  \n",
       "        mean  \n",
       "0  90.090909  \n",
       "1  84.000000  \n",
       "2  90.166667  \n",
       "3  72.000000  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Group data by Clusters (K=4)\n",
    "univ4.groupby('clusters4id').agg(['mean']).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ce068dffd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Clusters\n",
    "plt.figure(figsize=(10, 7))  \n",
    "plt.scatter(univ4['clusters4id'],univ4['SAT'], c=clusters4.labels_) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build Cluster algorithm using K=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=3, random_state=42)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cluster algorithm using K=3\n",
    "clusters3=KMeans(3,random_state=42).fit(univ_norm)\n",
    "clusters3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 1, 2, 1, 0, 2, 0, 2,\n",
       "       1, 1, 2])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusters3.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Univ</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "      <th>clusters3id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brown</td>\n",
       "      <td>1310</td>\n",
       "      <td>89</td>\n",
       "      <td>22</td>\n",
       "      <td>13</td>\n",
       "      <td>22704</td>\n",
       "      <td>94</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CalTech</td>\n",
       "      <td>1415</td>\n",
       "      <td>100</td>\n",
       "      <td>25</td>\n",
       "      <td>6</td>\n",
       "      <td>63575</td>\n",
       "      <td>81</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>CMU</td>\n",
       "      <td>1260</td>\n",
       "      <td>62</td>\n",
       "      <td>59</td>\n",
       "      <td>9</td>\n",
       "      <td>25026</td>\n",
       "      <td>72</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Columbia</td>\n",
       "      <td>1310</td>\n",
       "      <td>76</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>31510</td>\n",
       "      <td>88</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Cornell</td>\n",
       "      <td>1280</td>\n",
       "      <td>83</td>\n",
       "      <td>33</td>\n",
       "      <td>13</td>\n",
       "      <td>21864</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Dartmouth</td>\n",
       "      <td>1340</td>\n",
       "      <td>89</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>32162</td>\n",
       "      <td>95</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duke</td>\n",
       "      <td>1315</td>\n",
       "      <td>90</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>31585</td>\n",
       "      <td>95</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Georgetown</td>\n",
       "      <td>1255</td>\n",
       "      <td>74</td>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "      <td>20126</td>\n",
       "      <td>92</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Harvard</td>\n",
       "      <td>1400</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>39525</td>\n",
       "      <td>97</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>JohnsHopkins</td>\n",
       "      <td>1305</td>\n",
       "      <td>75</td>\n",
       "      <td>44</td>\n",
       "      <td>7</td>\n",
       "      <td>58691</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>MIT</td>\n",
       "      <td>1380</td>\n",
       "      <td>94</td>\n",
       "      <td>30</td>\n",
       "      <td>10</td>\n",
       "      <td>34870</td>\n",
       "      <td>91</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Northwestern</td>\n",
       "      <td>1260</td>\n",
       "      <td>85</td>\n",
       "      <td>39</td>\n",
       "      <td>11</td>\n",
       "      <td>28052</td>\n",
       "      <td>89</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NotreDame</td>\n",
       "      <td>1255</td>\n",
       "      <td>81</td>\n",
       "      <td>42</td>\n",
       "      <td>13</td>\n",
       "      <td>15122</td>\n",
       "      <td>94</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>PennState</td>\n",
       "      <td>1081</td>\n",
       "      <td>38</td>\n",
       "      <td>54</td>\n",
       "      <td>18</td>\n",
       "      <td>10185</td>\n",
       "      <td>80</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Princeton</td>\n",
       "      <td>1375</td>\n",
       "      <td>91</td>\n",
       "      <td>14</td>\n",
       "      <td>8</td>\n",
       "      <td>30220</td>\n",
       "      <td>95</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Purdue</td>\n",
       "      <td>1005</td>\n",
       "      <td>28</td>\n",
       "      <td>90</td>\n",
       "      <td>19</td>\n",
       "      <td>9066</td>\n",
       "      <td>69</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Stanford</td>\n",
       "      <td>1360</td>\n",
       "      <td>90</td>\n",
       "      <td>20</td>\n",
       "      <td>12</td>\n",
       "      <td>36450</td>\n",
       "      <td>93</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>TexasA&amp;M</td>\n",
       "      <td>1075</td>\n",
       "      <td>49</td>\n",
       "      <td>67</td>\n",
       "      <td>25</td>\n",
       "      <td>8704</td>\n",
       "      <td>67</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>UCBerkeley</td>\n",
       "      <td>1240</td>\n",
       "      <td>95</td>\n",
       "      <td>40</td>\n",
       "      <td>17</td>\n",
       "      <td>15140</td>\n",
       "      <td>78</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>UChicago</td>\n",
       "      <td>1290</td>\n",
       "      <td>75</td>\n",
       "      <td>50</td>\n",
       "      <td>13</td>\n",
       "      <td>38380</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>UMichigan</td>\n",
       "      <td>1180</td>\n",
       "      <td>65</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>15470</td>\n",
       "      <td>85</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>UPenn</td>\n",
       "      <td>1285</td>\n",
       "      <td>80</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>27553</td>\n",
       "      <td>90</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>UVA</td>\n",
       "      <td>1225</td>\n",
       "      <td>77</td>\n",
       "      <td>44</td>\n",
       "      <td>14</td>\n",
       "      <td>13349</td>\n",
       "      <td>92</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>UWisconsin</td>\n",
       "      <td>1085</td>\n",
       "      <td>40</td>\n",
       "      <td>69</td>\n",
       "      <td>15</td>\n",
       "      <td>11857</td>\n",
       "      <td>71</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Yale</td>\n",
       "      <td>1375</td>\n",
       "      <td>95</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>43514</td>\n",
       "      <td>96</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Univ   SAT  Top10  Accept  SFRatio  Expenses  GradRate  \\\n",
       "0          Brown  1310     89      22       13     22704        94   \n",
       "1        CalTech  1415    100      25        6     63575        81   \n",
       "2            CMU  1260     62      59        9     25026        72   \n",
       "3       Columbia  1310     76      24       12     31510        88   \n",
       "4        Cornell  1280     83      33       13     21864        90   \n",
       "5      Dartmouth  1340     89      23       10     32162        95   \n",
       "6           Duke  1315     90      30       12     31585        95   \n",
       "7     Georgetown  1255     74      24       12     20126        92   \n",
       "8        Harvard  1400     91      14       11     39525        97   \n",
       "9   JohnsHopkins  1305     75      44        7     58691        87   \n",
       "10           MIT  1380     94      30       10     34870        91   \n",
       "11  Northwestern  1260     85      39       11     28052        89   \n",
       "12     NotreDame  1255     81      42       13     15122        94   \n",
       "13     PennState  1081     38      54       18     10185        80   \n",
       "14     Princeton  1375     91      14        8     30220        95   \n",
       "15        Purdue  1005     28      90       19      9066        69   \n",
       "16      Stanford  1360     90      20       12     36450        93   \n",
       "17      TexasA&M  1075     49      67       25      8704        67   \n",
       "18    UCBerkeley  1240     95      40       17     15140        78   \n",
       "19      UChicago  1290     75      50       13     38380        87   \n",
       "20     UMichigan  1180     65      68       16     15470        85   \n",
       "21         UPenn  1285     80      36       11     27553        90   \n",
       "22           UVA  1225     77      44       14     13349        92   \n",
       "23    UWisconsin  1085     40      69       15     11857        71   \n",
       "24          Yale  1375     95      19       11     43514        96   \n",
       "\n",
       "    clusters3id  \n",
       "0             0  \n",
       "1             2  \n",
       "2             2  \n",
       "3             2  \n",
       "4             0  \n",
       "5             2  \n",
       "6             2  \n",
       "7             0  \n",
       "8             2  \n",
       "9             2  \n",
       "10            2  \n",
       "11            2  \n",
       "12            0  \n",
       "13            1  \n",
       "14            2  \n",
       "15            1  \n",
       "16            2  \n",
       "17            1  \n",
       "18            0  \n",
       "19            2  \n",
       "20            0  \n",
       "21            2  \n",
       "22            1  \n",
       "23            1  \n",
       "24            2  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assign clusters to the data set\n",
    "univ3=univ.copy()\n",
    "univ3['clusters3id']=clusters3.labels_\n",
    "univ3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.97772342e-02, 4.52559527e-03, 2.24130914e-03, 7.94542102e-04,\n",
       "        9.97478703e-01, 4.93538672e-03],\n",
       "       [1.04154971e-01, 4.29384696e-03, 6.37080088e-03, 1.79892035e-03,\n",
       "        9.94428119e-01, 7.16777365e-03],\n",
       "       [3.81314072e-02, 2.41988834e-03, 8.98489564e-04, 2.98809935e-04,\n",
       "        9.99232220e-01, 2.57348899e-03]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the centroids for K=3 clusters with 6 variables\n",
    "clusters3.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>clusters3id</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Top10</th>\n",
       "      <th>Accept</th>\n",
       "      <th>SFRatio</th>\n",
       "      <th>Expenses</th>\n",
       "      <th>GradRate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "      <th>mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1253.333333</td>\n",
       "      <td>81.166667</td>\n",
       "      <td>38.166667</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>18404.333333</td>\n",
       "      <td>88.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1094.200000</td>\n",
       "      <td>46.400000</td>\n",
       "      <td>64.800000</td>\n",
       "      <td>18.200000</td>\n",
       "      <td>10632.200000</td>\n",
       "      <td>75.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1333.571429</td>\n",
       "      <td>85.214286</td>\n",
       "      <td>30.500000</td>\n",
       "      <td>10.214286</td>\n",
       "      <td>37222.357143</td>\n",
       "      <td>89.714286</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  clusters3id          SAT      Top10     Accept    SFRatio      Expenses  \\\n",
       "                      mean       mean       mean       mean          mean   \n",
       "0           0  1253.333333  81.166667  38.166667  14.000000  18404.333333   \n",
       "1           1  1094.200000  46.400000  64.800000  18.200000  10632.200000   \n",
       "2           2  1333.571429  85.214286  30.500000  10.214286  37222.357143   \n",
       "\n",
       "    GradRate  \n",
       "        mean  \n",
       "0  88.833333  \n",
       "1  75.800000  \n",
       "2  89.714286  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Group data by Clusters (K=3)\n",
    "univ3.groupby('clusters3id').agg(['mean']).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ce06911fd0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Clusters\n",
    "plt.figure(figsize=(10, 7))  \n",
    "plt.scatter(univ3['clusters3id'],univ3['SAT'], c=clusters3.labels_) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}