Geometry EDA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Geometry Common Core Regents Exam EDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook will be the exploratory data analysis done to determine any possible consistences and patterns in the questions of the Geometry CC Regents exam. Specifically, we are trying to answer:\n",
    "\n",
    "* Is the frequency of each cluster of questions consistent through exam?\n",
    "* Does the frequency of each cluster hold true with the [engageny guidelines](https://www.engageny.org/resource/regents-exams-mathematics-geometry-test-guide/file/96826)?\n",
    "* Are there clusters being skipped? If so why and is there consistence with those omissions?\n",
    "* Which clusters in a domain are more widely assessed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sqlalchemy import create_engine, MetaData, Table, select\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the data from Postgresql"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create engine\n",
    "engine = create_engine('postgresql+psycopg2://postgres:password@localhost:####/Regents Exams DataBase')\n",
    "\n",
    "# connection\n",
    "conn = engine.connect()\n",
    "\n",
    "# acquire table\n",
    "metadata = MetaData()\n",
    "sql_table = Table('Geometry', metadata, autoload=True, autoload_with=engine)\n",
    "\n",
    "# assign query to a variable with python sqlalchemy select\n",
    "results = conn.execute(select([sql_table])).fetchall()\n",
    "\n",
    "df = pd.DataFrame(results, columns=sql_table.columns.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminary Checks of Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>ClusterTitle</th>\n",
       "      <th>Cluster</th>\n",
       "      <th>Regents Date</th>\n",
       "      <th>Type</th>\n",
       "      <th>DateFixed</th>\n",
       "      <th>Qnumber</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Visualize relationships between two-dimensiona...</td>\n",
       "      <td>G-GMD.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Understand congruence in terms of rigid motions</td>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Use coordinates to prove simple geometric theo...</td>\n",
       "      <td>G-GPE.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Experiment with transformations in the plane</td>\n",
       "      <td>G-CO.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Define trigonometric ratios and solve problems...</td>\n",
       "      <td>G-SRT.C</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   id                                       ClusterTitle  Cluster  \\\n",
       "0   1  Visualize relationships between two-dimensiona...  G-GMD.B   \n",
       "1   2    Understand congruence in terms of rigid motions   G-CO.B   \n",
       "2   3  Use coordinates to prove simple geometric theo...  G-GPE.B   \n",
       "3   4       Experiment with transformations in the plane   G-CO.A   \n",
       "4   5  Define trigonometric ratios and solve problems...  G-SRT.C   \n",
       "\n",
       "  Regents Date Type DateFixed Qnumber  \n",
       "0   2015-06-01   MC    Jun-15       1  \n",
       "1   2015-06-01   MC    Jun-15       2  \n",
       "2   2015-06-01   MC    Jun-15       3  \n",
       "3   2015-06-01   MC    Jun-15       4  \n",
       "4   2015-06-01   MC    Jun-15       5  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check data\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 358 entries, 0 to 357\n",
      "Data columns (total 7 columns):\n",
      "id              358 non-null int64\n",
      "ClusterTitle    358 non-null object\n",
      "Cluster         358 non-null object\n",
      "Regents Date    358 non-null object\n",
      "Type            358 non-null object\n",
      "DateFixed       358 non-null object\n",
      "Qnumber         358 non-null object\n",
      "dtypes: int64(1), object(6)\n",
      "memory usage: 19.7+ KB\n"
     ]
    }
   ],
   "source": [
    "# Check dataframe info\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 358 entries, 0 to 357\n",
      "Data columns (total 7 columns):\n",
      "id              358 non-null int64\n",
      "ClusterTitle    358 non-null object\n",
      "Cluster         358 non-null object\n",
      "Regents Date    358 non-null object\n",
      "Type            358 non-null object\n",
      "DateFixed       358 non-null object\n",
      "Qnumber         358 non-null object\n",
      "dtypes: int64(1), object(6)\n",
      "memory usage: 139.9 KB\n"
     ]
    }
   ],
   "source": [
    "# get exact memory usage of data frame\n",
    "df.info(memory_usage='deep')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index              80\n",
       "id               2864\n",
       "ClusterTitle    38222\n",
       "Cluster         22713\n",
       "Regents Date    14320\n",
       "Type            21122\n",
       "DateFixed       22554\n",
       "Qnumber         21392\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check exact memory usage of each column\n",
    "df.memory_usage(deep=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't need the id since that was only created for SQL table. Will drop this now to reduce memory usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop id column\n",
    "df.drop(['id'],axis='columns',inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 358 entries, 0 to 357\n",
      "Data columns (total 6 columns):\n",
      "ClusterTitle    358 non-null object\n",
      "Cluster         358 non-null object\n",
      "Regents Date    358 non-null object\n",
      "Type            358 non-null object\n",
      "DateFixed       358 non-null object\n",
      "Qnumber         358 non-null object\n",
      "dtypes: object(6)\n",
      "memory usage: 137.1 KB\n"
     ]
    }
   ],
   "source": [
    "# check if column was dropped and for memory\n",
    "df.info(memory_usage='deep')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.8 KB less memory used. Let's check out the exact memory usage of each column in bytes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'str'>\n",
      "<class 'str'>\n",
      "<class 'datetime.date'>\n",
      "<class 'str'>\n",
      "<class 'str'>\n",
      "<class 'str'>\n"
     ]
    }
   ],
   "source": [
    "# Get exact types of each column\n",
    "for column in df.columns:\n",
    "    print(type(df[column][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change Cluster column to category type\n",
    "df['Cluster']=df['Cluster'].astype('category')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index              80\n",
       "ClusterTitle    38222\n",
       "Cluster          1885\n",
       "Regents Date    14320\n",
       "Type            21122\n",
       "DateFixed       22554\n",
       "Qnumber         21392\n",
       "dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# See memory reduction in category column\n",
    "df.memory_usage(deep=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Memory usage for Cluster column reduced significantly. Lets do the same for the Type (2 labels) and the Qnumber(36 labels) columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change Type and Qnumber data types into categorical\n",
    "df['Type']=df['Type'].astype('category')\n",
    "df['Qnumber']=df['Qnumber'].astype('category')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index              80\n",
       "ClusterTitle    38222\n",
       "Cluster          1885\n",
       "Regents Date    14320\n",
       "Type              556\n",
       "DateFixed       22554\n",
       "Qnumber          3789\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see memory changes\n",
    "df.memory_usage(deep=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ClusterTitle      object\n",
       "Cluster         category\n",
       "Regents Date      object\n",
       "Type            category\n",
       "DateFixed         object\n",
       "Qnumber         category\n",
       "dtype: object"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 358 entries, 0 to 357\n",
      "Data columns (total 6 columns):\n",
      "ClusterTitle    358 non-null object\n",
      "Cluster         358 non-null category\n",
      "Regents Date    358 non-null object\n",
      "Type            358 non-null category\n",
      "DateFixed       358 non-null object\n",
      "Qnumber         358 non-null category\n",
      "dtypes: category(3), object(3)\n",
      "memory usage: 79.5 KB\n"
     ]
    }
   ],
   "source": [
    "# see total memory change\n",
    "df.info(memory_usage='deep')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "About a 42% reduction in memory usage of the data frame."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get Cluster totals\n",
    "cluster_totals=df['Cluster'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OAI4DDmyzHQgcO64YJEmSJGldMs4mmlsDn04ysZ2PVtUXknwX+HiSg4ALgKeNMQZJkiRJ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\nSZIkSeoJEzxJkiRJ6on/D3546aU/AB4PAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bar chart for overall count of each cluster throughout all the exams given\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(x = cluster_totals.index,height=cluster_totals)\n",
    "plt.title('Total Number of Questions for All Exams per Cluster')\n",
    "plt.xlabel('Cluster')\n",
    "plt.ylabel('Total # of Questions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So in total G-CO.C had the most questions across all exams. This followed by G-SRT C & B and GPE.B.\n",
    "Lets see the totals both by question Type (Multiple Choice and by Constructed Response). Then we will look at these totals by year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up values\n",
    "cluster_totals_MC=df['Cluster'][df.Type=='MC'].value_counts()\n",
    "cluster_totals_CR=df['Cluster'][df.Type=='CR'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JkiRJGsVIP3ReVeeOKxBJkiRJ0vyMlOBJkiRJktZew9yDJ0nSnC0/8tRJhzCS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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# multiple choice cluster totals\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(x = cluster_totals_MC.index,height=cluster_totals_MC)\n",
    "plt.title('Total Multiple Choice Questions for All Exams per Cluster')\n",
    "plt.xlabel('Cluster')\n",
    "plt.ylabel('Total # of MC Questions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V7QPsM591SJIkSZJua5AWvCuSPCe32gW4YtiBSZIkSZJmZ5AE70XAC4DfA5cB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\njvj/F4Lc86QtM3kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# multiple choice cluster totals\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(x = cluster_totals_CR.index,height=cluster_totals_CR, color='orange')\n",
    "plt.title('Total Constructed Response Questions for All Exams per Cluster')\n",
    "plt.xlabel('Cluster')\n",
    "plt.ylabel('Total # of CR Questions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Across all exams:\n",
    "* G-CO.C had the most total MC questions.\n",
    "* G-SRT.C had the most total CR questions.\n",
    "* G-CO.D is never assessed as a MC question. This makes sense since these are geometric constructions.\n",
    "* G-GMD.B (cross sections of 3D figures) is never assessed as a CR question.\n",
    "<br/>\n",
    "\n",
    "There are instances in both question types where there are a small group of clusters that have approximately the same number of total questions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sort both series by index alphabetically\n",
    "cluster_totals_MC=cluster_totals_MC.sort_index()\n",
    "cluster_totals_CR=cluster_totals_CR.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GGFP7lNggqepkYLKI3Kuqf6vEOhljjKmFAhllN1VEfsuZ2HUfA6+o6smg1coY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\n51wq/B+NS95W3vgxIQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  comparing the totals of MC to CR by\n",
    "plt.scatter(x=cluster_totals_MC,y=cluster_totals_CR)\n",
    "for i, txt in enumerate(cluster_totals_MC.index):\n",
    "    plt.annotate(txt,(cluster_totals_MC[i],cluster_totals_CR[i]))\n",
    "plt.title('Scatterplot Comparing Total MC questions to Total CR Questions')\n",
    "plt.xlabel('Multiple Choice Totals')\n",
    "plt.ylabel('Constructed Response Totals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Doesn't appear to be any strong correlation. Although there are about 4-5 clusters that appear to form a line with their coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44187960335255883"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Using corr method to determine the correlation\n",
    "cluster_totals_MC.corr(cluster_totals_CR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the correlation coefficient is less than .5, there is a weak positive correlation between total number of mc questions vs total number of cr questions for each cluster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to view these totals by exam date."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'10 exams given'"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get total number of exams. (Note this is better in one line without variable memory wise. But I wanted to try out the f string\n",
    "# in python)\n",
    "total_exams=len(df['Regents Date'].unique())\n",
    "f'{total_exams} exams given'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x2160 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Since there are 10 exams, my subplots will be created with 10 rows (one for each exam), and two columns(MC and CR)\n",
    "f,ax=plt.subplots(10,2, figsize=(30,30))\n",
    "\n",
    "# now to fill in our plots\n",
    "for i, exam in enumerate(df['DateFixed'].unique()):\n",
    "    plot_exam=df['Cluster'][df.DateFixed==exam]\n",
    "    MC=plot_exam[df.Type=='MC'].value_counts()\n",
    "    CR=plot_exam[df.Type=='CR'].value_counts()\n",
    "    ax[i,0].bar(x=MC.index,height=MC)\n",
    "    ax[i,0].set_title(f'{exam} MC Totals')\n",
    "    ax[i,1].bar(x=CR.index,height=CR,color ='orange')\n",
    "    ax[i,1].set_title(f'{exam} CR Totals')\n",
    "\n",
    "# sub plot adjustments\n",
    "f.subplots_adjust(top=.99, bottom=0.01, wspace=0.2,hspace=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CR_freq</th>\n",
       "      <th>Cluster</th>\n",
       "      <th>MC_freq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>G-C.A</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>G-C.B</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>G-CO.A</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>G-CO.C</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CR_freq Cluster  MC_freq\n",
       "0        0   G-C.A        1\n",
       "1        1   G-C.B        0\n",
       "2        0  G-CO.A        2\n",
       "3        1  G-CO.B        2\n",
       "4        3  G-CO.C        2"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make data frame with columns=[cluster, # of MC, # of CR] to see if there is a correlation between the number of MC and CR\n",
    "# questions across the exam.\n",
    "\n",
    "# initiate columns\n",
    "data={'Cluster' : [],\n",
    "    'MC_freq':[],\n",
    "    'CR_freq': []}\n",
    "\n",
    "# get data into initialized columns\n",
    "for exam in df['DateFixed'].unique():\n",
    "    plot_exam=df['Cluster'][df.DateFixed==exam]\n",
    "    MC=plot_exam[df.Type=='MC'].value_counts().sort_index()\n",
    "    CR=plot_exam[df.Type=='CR'].value_counts().sort_index()\n",
    "    for i in range(len(MC)):\n",
    "        data['Cluster'].append(MC.index[i])\n",
    "        data['MC_freq'].append(MC[i])\n",
    "        data['CR_freq'].append(CR[i])\n",
    "\n",
    "\n",
    "\n",
    "# create data frame and check\n",
    "q_points=pd.DataFrame(data=data)\n",
    "q_points.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F2uleJH3Pr9CFZvMR8QdSXf0E0nKsx9L1yyeSDv6zJe1FarQwmFQlchd53XZhvvMj/a5l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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x=q_points['MC_freq'],y=q_points['CR_freq'])\n",
    "#for i, txt in enumerate(q_points['Cluster']):\n",
    "    #plt.annotate(txt,(cluster_totals_MC[i],cluster_totals_CR[i]))\n",
    "plt.title('Scatterplot Comparing Total MC questions to Total CR Questions')\n",
    "plt.xlabel('Multiple Choice Totals')\n",
    "plt.ylabel('Constructed Response Totals')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.037191189016248717"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# correlation between multiple choice and constructed response questions (clearly none but lets get the exact value)\n",
    "q_points['MC_freq'].corr(q_points['CR_freq'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As was proved by the `corr` method, there is not correlation between the number of multiple choices and constructed response questions for each cluster from any exam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sabal\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1876fe9b748>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kuP/67YOsP1jDd++4gLxUrcoooRUTHcUPl83n2y/v4hdvHeTNshN89V2zuXx6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\niHiQwl1ExIP+Px4BTzKMQRhaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Checking the distribution of number of multiple choice questions\n",
    "sns.distplot(q_points['MC_freq'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sabal\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x187724ed7b8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6XsNPPzlZq+2JZ0RH+Pn9LdOZM6Yl4E8vXS3epnBvtWpfOQ+tPMDnZucyY7jW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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# doing the same for constructed response\n",
    "sns.distplot(q_points['CR_freq'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neither plot seems to follow a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18770176ba8>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2Ldu37iFhH/rzVWMeG2l6rG6dOVtEQ+5nu7VnzyNfOaw7WKv/nuq2mx5HWhsX+LF/LOvo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\nIPABoBAEPgAUgsAHgEIQ+ABQiP8DMW/N2DAammYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# looking at a bivariate kde plot with the quantity of multiple choice and constructed response\n",
    "sns.kdeplot(q_points['MC_freq'],q_points['CR_freq'],shade=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our most dense area is where one multiple choice question is asked and no constructed response questions are asked during an exam. We should see which clusters had that pair."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "G-GPE.A    8\n",
       "G-C.B      6\n",
       "G-GMD.B    6\n",
       "G-GMD.A    4\n",
       "G-CO.B     2\n",
       "G-C.A      2\n",
       "G-CO.A     1\n",
       "Name: Cluster, dtype: int64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get clusters than satisfy the dense kde area on our above plot and get their totals.\n",
    "one_zero_clusters=q_points['Cluster'][(q_points.MC_freq==1) & (q_points.CR_freq==0)]\n",
    "one_zero_clusters.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "G-GPE.A - [ 'Translate between the geometric description and the equation for a conic section']\n",
      "G-C.B - ['Find arc lengths and areas of sectors of circles']\n",
      "G-GMD.B - [ 'Visualize relationships between two-dimensional and three-dimensional objects']\n",
      "G-GMD.A - ['Explain volume formulas and use them to solve problems']\n",
      "G-CO.B - ['Understand congruence in terms of rigid motions']\n",
      "G-C.A - ['Understand and apply theorems about circles']\n",
      "G-CO.A - ['Experiment with transformations in the plane']\n"
     ]
    }
   ],
   "source": [
    "# Seeing the descriptions for these clusters\n",
    "for cluster in one_zero_clusters.value_counts().index:\n",
    "    title=df['ClusterTitle'][df.Cluster==cluster].unique()\n",
    "    print(f'{cluster} - {title}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18770176ef0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hDeCLB07h4G3qacjBpHr4twNaxm1oAzj12EZ23j5Pb2EFKzoe5/Tjm2pdUqp2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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot question frequencies by mc\n",
    "plt.figure(figsize=(15,5))\n",
    "sns.set(style=\"whitegrid\")\n",
    "sns.boxplot(data=q_points[['Cluster','MC_freq']],x=q_points['Cluster'],y=q_points['MC_freq'])\n",
    "sns.stripplot(data=q_points[['Cluster','MC_freq']],x=q_points['Cluster'],y=q_points['MC_freq'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots are not all true box plots (such as the one for G-C.A) due to the discrete nature of the data. Some of the question densities are right skewed(G-C0.C) and left skewed (G-SRT.B). We also see that some of the clusters are consistent with their frequency (such as G-C.A, G-CO.D) but there are many with outliers (such as G-CO.B, G-SRT.A, and G-GPE.A).This is concerning because depending on the corresponding frequencies with the clusters' constructed response questions there many be inconsistency with following the guidelines of engageny."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1876fe80c88>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p8dDnu2WvQL8JCQkqch3SiFvMf5qO6hraWyReWOVRVHxC0L2a+VnTVe+1Cph2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\n3IoJAAAAABZHsAMAAAAAiyP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      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot question frequencies by CR\n",
    "plt.figure(figsize=(15,5))\n",
    "sns.boxplot(data=q_points[['Cluster','CR_freq']],x=q_points['Cluster'],y=q_points['CR_freq'])\n",
    "sns.stripplot(data=q_points[['Cluster','CR_freq']],x=q_points['Cluster'],y=q_points['CR_freq'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking again at the data from the CR prespective. Some of the question densities are right skewed(G-C0.A and G-SRT.C). We also see that some of the clusters are consistent with their frequency (such as G-C.A,G-C.B G-CO.D, G-MG.A) but there are many with outliers (such as G-CO.D, G-SRT.A, and G-GPE.A). Lets check out the percentages for each cluster both with all exams and then per examination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sabal\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "# Create percentage bar chart for clusters across all exams.First going to feature engineer\n",
    "df['freq'] = df.groupby('Cluster')['Cluster'].transform('count')\n",
    "        \n",
    "# drop duplicates\n",
    "new_df = df.drop_duplicates(subset=['Cluster'], keep='first')\n",
    "        \n",
    "# percentage of exam column\n",
    "new_df['freq_pct'] = new_df['freq'].apply(lambda x: x/sum(new_df['freq']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cluster</th>\n",
       "      <th>freq_pct</th>\n",
       "      <th>ClusterTitle</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>G-GMD.B</td>\n",
       "      <td>0.039106</td>\n",
       "      <td>Visualize relationships between two-dimensiona...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>0.069832</td>\n",
       "      <td>Understand congruence in terms of rigid motions</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>G-GPE.B</td>\n",
       "      <td>0.108939</td>\n",
       "      <td>Use coordinates to prove simple geometric theo...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>G-CO.A</td>\n",
       "      <td>0.069832</td>\n",
       "      <td>Experiment with transformations in the plane</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>G-SRT.C</td>\n",
       "      <td>0.111732</td>\n",
       "      <td>Define trigonometric ratios and solve problems...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>G-MG.A</td>\n",
       "      <td>0.083799</td>\n",
       "      <td>Apply geometric concepts in modeling situations</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>G-SRT.B</td>\n",
       "      <td>0.108939</td>\n",
       "      <td>Prove theorems involving similarity</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>G-CO.C</td>\n",
       "      <td>0.139665</td>\n",
       "      <td>Prove geometric theorems</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>G-GPE.A</td>\n",
       "      <td>0.030726</td>\n",
       "      <td>Translate between the geometric description an...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>G-SRT.A</td>\n",
       "      <td>0.089385</td>\n",
       "      <td>Understand similarity in terms of similarity t...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>G-C.A</td>\n",
       "      <td>0.050279</td>\n",
       "      <td>Understand and apply theorems about circles</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>G-GMD.A</td>\n",
       "      <td>0.036313</td>\n",
       "      <td>Explain volume formulas and use them to solve ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>G-CO.D</td>\n",
       "      <td>0.030726</td>\n",
       "      <td>Make geometric constructions</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>G-C.B</td>\n",
       "      <td>0.030726</td>\n",
       "      <td>Find arc lengths and areas of sectors of circles</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Cluster  freq_pct                                       ClusterTitle\n",
       "0   G-GMD.B  0.039106  Visualize relationships between two-dimensiona...\n",
       "1    G-CO.B  0.069832    Understand congruence in terms of rigid motions\n",
       "2   G-GPE.B  0.108939  Use coordinates to prove simple geometric theo...\n",
       "3    G-CO.A  0.069832       Experiment with transformations in the plane\n",
       "4   G-SRT.C  0.111732  Define trigonometric ratios and solve problems...\n",
       "6    G-MG.A  0.083799    Apply geometric concepts in modeling situations\n",
       "7   G-SRT.B  0.108939                Prove theorems involving similarity\n",
       "12   G-CO.C  0.139665                           Prove geometric theorems\n",
       "13  G-GPE.A  0.030726  Translate between the geometric description an...\n",
       "17  G-SRT.A  0.089385  Understand similarity in terms of similarity t...\n",
       "19    G-C.A  0.050279        Understand and apply theorems about circles\n",
       "22  G-GMD.A  0.036313  Explain volume formulas and use them to solve ...\n",
       "24   G-CO.D  0.030726                       Make geometric constructions\n",
       "28    G-C.B  0.030726   Find arc lengths and areas of sectors of circles"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the data with the clusters and percentage changes\n",
    "new_df[['Cluster','freq_pct','ClusterTitle']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qKytLycnJCgoK0s0332xd8StfvryOHz/uURMhISEezecELpfLsf0Wi95s+APT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\n7AEAAFSQ2AMAAKggsQcAAFBBPwFe3QGOXkXLeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ploting percentage bar\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(x=new_df['Cluster'],height=new_df['freq_pct'])\n",
    "plt.title('Percentage by Cluster of All Exams as of June 2018')\n",
    "plt.xlabel('Cluster')\n",
    "plt.ylabel('Percentage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Cluster              ClusterTitle\n",
      "12  G-CO.C  Prove geometric theorems\n"
     ]
    }
   ],
   "source": [
    "# getting max percentage\n",
    "print(new_df[new_df.freq_pct==new_df.freq_pct.max()][['Cluster','ClusterTitle']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Cluster                                       ClusterTitle\n",
      "13  G-GPE.A  Translate between the geometric description an...\n",
      "24   G-CO.D                       Make geometric constructions\n",
      "28    G-C.B   Find arc lengths and areas of sectors of circles\n",
      "0.0307262569832\n"
     ]
    }
   ],
   "source": [
    "# min percetage\n",
    "print(new_df[new_df.freq_pct==new_df.freq_pct.min()][['Cluster','ClusterTitle']])\n",
    "print(new_df.freq_pct.min())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 Clusters at the min percentage of about 3.1%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check out the percentages on each exam and see if they are consistent with the engageny guidelines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ClusterTitle</th>\n",
       "      <th>Cluster</th>\n",
       "      <th>Regents Date</th>\n",
       "      <th>Type</th>\n",
       "      <th>DateFixed</th>\n",
       "      <th>Qnumber</th>\n",
       "      <th>freq</th>\n",
       "      <th>Domain</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Visualize relationships between two-dimensiona...</td>\n",
       "      <td>G-GMD.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>G-GMD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Understand congruence in terms of rigid motions</td>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>2</td>\n",
       "      <td>25</td>\n",
       "      <td>G-CO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Use coordinates to prove simple geometric theo...</td>\n",
       "      <td>G-GPE.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>3</td>\n",
       "      <td>39</td>\n",
       "      <td>G-GPE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Experiment with transformations in the plane</td>\n",
       "      <td>G-CO.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>4</td>\n",
       "      <td>25</td>\n",
       "      <td>G-CO</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Define trigonometric ratios and solve problems...</td>\n",
       "      <td>G-SRT.C</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>5</td>\n",
       "      <td>40</td>\n",
       "      <td>G-SRT</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                        ClusterTitle  Cluster Regents Date  \\\n",
       "0  Visualize relationships between two-dimensiona...  G-GMD.B   2015-06-01   \n",
       "1    Understand congruence in terms of rigid motions   G-CO.B   2015-06-01   \n",
       "2  Use coordinates to prove simple geometric theo...  G-GPE.B   2015-06-01   \n",
       "3       Experiment with transformations in the plane   G-CO.A   2015-06-01   \n",
       "4  Define trigonometric ratios and solve problems...  G-SRT.C   2015-06-01   \n",
       "\n",
       "  Type DateFixed Qnumber  freq Domain  \n",
       "0   MC    Jun-15       1    14  G-GMD  \n",
       "1   MC    Jun-15       2    25   G-CO  \n",
       "2   MC    Jun-15       3    39  G-GPE  \n",
       "3   MC    Jun-15       4    25   G-CO  \n",
       "4   MC    Jun-15       5    40  G-SRT  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First we need to create a column for our data that classifies our clusters into their domains. This is the text prior to the \n",
    "# period in the cluster label. We will then check the results\n",
    "df['Domain']=df['Cluster'].apply(lambda x: x[:-2])\n",
    "df.head()\n",
    "# success"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sabal\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "# Create percentage bar chart for Domains across all exams. First going to feature engineer\n",
    "df['Domain_freq'] = df.groupby('Domain')['Domain'].transform('count')\n",
    "        \n",
    "# drop duplicates\n",
    "domain_df = df.drop_duplicates(subset=['Domain'], keep='first')\n",
    "        \n",
    "# percentage of exam column\n",
    "domain_df['freq_pct'] = domain_df['Domain_freq'].apply(lambda x: x/sum(domain_df['Domain_freq']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ClusterTitle</th>\n",
       "      <th>Cluster</th>\n",
       "      <th>Regents Date</th>\n",
       "      <th>Type</th>\n",
       "      <th>DateFixed</th>\n",
       "      <th>Qnumber</th>\n",
       "      <th>freq</th>\n",
       "      <th>Domain</th>\n",
       "      <th>Domain_freq</th>\n",
       "      <th>freq_pct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Visualize relationships between two-dimensiona...</td>\n",
       "      <td>G-GMD.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>G-GMD</td>\n",
       "      <td>27</td>\n",
       "      <td>0.075419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Understand congruence in terms of rigid motions</td>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>2</td>\n",
       "      <td>25</td>\n",
       "      <td>G-CO</td>\n",
       "      <td>111</td>\n",
       "      <td>0.310056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Use coordinates to prove simple geometric theo...</td>\n",
       "      <td>G-GPE.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>3</td>\n",
       "      <td>39</td>\n",
       "      <td>G-GPE</td>\n",
       "      <td>50</td>\n",
       "      <td>0.139665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Define trigonometric ratios and solve problems...</td>\n",
       "      <td>G-SRT.C</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>5</td>\n",
       "      <td>40</td>\n",
       "      <td>G-SRT</td>\n",
       "      <td>111</td>\n",
       "      <td>0.310056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Apply geometric concepts in modeling situations</td>\n",
       "      <td>G-MG.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>7</td>\n",
       "      <td>30</td>\n",
       "      <td>G-MG</td>\n",
       "      <td>30</td>\n",
       "      <td>0.083799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Understand and apply theorems about circles</td>\n",
       "      <td>G-C.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>20</td>\n",
       "      <td>18</td>\n",
       "      <td>G-C</td>\n",
       "      <td>29</td>\n",
       "      <td>0.081006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         ClusterTitle  Cluster Regents Date  \\\n",
       "0   Visualize relationships between two-dimensiona...  G-GMD.B   2015-06-01   \n",
       "1     Understand congruence in terms of rigid motions   G-CO.B   2015-06-01   \n",
       "2   Use coordinates to prove simple geometric theo...  G-GPE.B   2015-06-01   \n",
       "4   Define trigonometric ratios and solve problems...  G-SRT.C   2015-06-01   \n",
       "6     Apply geometric concepts in modeling situations   G-MG.A   2015-06-01   \n",
       "19        Understand and apply theorems about circles    G-C.A   2015-06-01   \n",
       "\n",
       "   Type DateFixed Qnumber  freq Domain  Domain_freq  freq_pct  \n",
       "0    MC    Jun-15       1    14  G-GMD           27  0.075419  \n",
       "1    MC    Jun-15       2    25   G-CO          111  0.310056  \n",
       "2    MC    Jun-15       3    39  G-GPE           50  0.139665  \n",
       "4    MC    Jun-15       5    40  G-SRT          111  0.310056  \n",
       "6    MC    Jun-15       7    30   G-MG           30  0.083799  \n",
       "19   MC    Jun-15      20    18    G-C           29  0.081006  "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check domain_df. Should have six rows\n",
    "domain_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ClusterTitle</th>\n",
       "      <th>Cluster</th>\n",
       "      <th>Regents Date</th>\n",
       "      <th>Type</th>\n",
       "      <th>DateFixed</th>\n",
       "      <th>Qnumber</th>\n",
       "      <th>freq</th>\n",
       "      <th>Domain</th>\n",
       "      <th>Domain_freq</th>\n",
       "      <th>freq_pct</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Understand congruence in terms of rigid motions</td>\n",
       "      <td>G-CO.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>2</td>\n",
       "      <td>25</td>\n",
       "      <td>G-CO</td>\n",
       "      <td>111</td>\n",
       "      <td>0.310056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Define trigonometric ratios and solve problems...</td>\n",
       "      <td>G-SRT.C</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>5</td>\n",
       "      <td>40</td>\n",
       "      <td>G-SRT</td>\n",
       "      <td>111</td>\n",
       "      <td>0.310056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Use coordinates to prove simple geometric theo...</td>\n",
       "      <td>G-GPE.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>3</td>\n",
       "      <td>39</td>\n",
       "      <td>G-GPE</td>\n",
       "      <td>50</td>\n",
       "      <td>0.139665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Apply geometric concepts in modeling situations</td>\n",
       "      <td>G-MG.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>7</td>\n",
       "      <td>30</td>\n",
       "      <td>G-MG</td>\n",
       "      <td>30</td>\n",
       "      <td>0.083799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Understand and apply theorems about circles</td>\n",
       "      <td>G-C.A</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>20</td>\n",
       "      <td>18</td>\n",
       "      <td>G-C</td>\n",
       "      <td>29</td>\n",
       "      <td>0.081006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Visualize relationships between two-dimensiona...</td>\n",
       "      <td>G-GMD.B</td>\n",
       "      <td>2015-06-01</td>\n",
       "      <td>MC</td>\n",
       "      <td>Jun-15</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>G-GMD</td>\n",
       "      <td>27</td>\n",
       "      <td>0.075419</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         ClusterTitle  Cluster Regents Date  \\\n",
       "1     Understand congruence in terms of rigid motions   G-CO.B   2015-06-01   \n",
       "4   Define trigonometric ratios and solve problems...  G-SRT.C   2015-06-01   \n",
       "2   Use coordinates to prove simple geometric theo...  G-GPE.B   2015-06-01   \n",
       "6     Apply geometric concepts in modeling situations   G-MG.A   2015-06-01   \n",
       "19        Understand and apply theorems about circles    G-C.A   2015-06-01   \n",
       "0   Visualize relationships between two-dimensiona...  G-GMD.B   2015-06-01   \n",
       "\n",
       "   Type DateFixed Qnumber  freq Domain  Domain_freq  freq_pct  \n",
       "1    MC    Jun-15       2    25   G-CO          111  0.310056  \n",
       "4    MC    Jun-15       5    40  G-SRT          111  0.310056  \n",
       "2    MC    Jun-15       3    39  G-GPE           50  0.139665  \n",
       "6    MC    Jun-15       7    30   G-MG           30  0.083799  \n",
       "19   MC    Jun-15      20    18    G-C           29  0.081006  \n",
       "0    MC    Jun-15       1    14  G-GMD           27  0.075419  "
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#will sort first by percentage\n",
    "\n",
    "domain_df=domain_df.sort_values(by=['freq_pct'],ascending=False)\n",
    "domain_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAIDSuWjY8/Pzk5+fn2bNmqXt27fr+PHjMsZIkjIyMtSoUaMrUiQAAAAA4M9x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\nAAAAACyIsAcAAAAAFvR/9l3wWROSbEcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ploting domain percentage bar\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.bar(x=domain_df['Domain'],height=domain_df['freq_pct'])\n",
    "plt.title('Percentage by Cluster of All Exams as of June 2018')\n",
    "plt.xlabel('Domain')\n",
    "plt.ylabel('Percentage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Placing the culumative percentages against the provided ranges:\n",
    "* G-CO is within range (27%–34%)\n",
    "* G-SRT is within range (29%–37%)\n",
    "* G-GPE is within range (12%–18%)\n",
    "* G-MG is within range (8%–15%)\n",
    "* G-C exceeds the range by about .1% (2%–8%)\n",
    "* G-GMD is within range (2%–8%)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we should check on the percentages per each exam "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Sabal\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:19: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x6480 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get domain percentages per exam and chart them\n",
    "\n",
    "# set different colors for each plot\n",
    "number_of_colors = 10\n",
    "\n",
    "color = [\"#\"+''.join([random.choice('0123456789ABCDEF') for j in range(6)])\n",
    "             for i in range(number_of_colors)]\n",
    "\n",
    "# set up sub plots\n",
    "f,ax=plt.subplots(10, figsize=(30,90))\n",
    "\n",
    "# loop through and plot on sub plot\n",
    "for i,date in enumerate(df['DateFixed'].unique()): \n",
    "    \n",
    "        # filter to date\n",
    "        sel_exam = df[df['DateFixed'] == date]\n",
    "\n",
    "        # create count column for sel_exam df\n",
    "        sel_exam['Domain_freq'] = sel_exam.groupby('Domain')['Domain'].transform('count')\n",
    "\n",
    "        # drop duplicates\n",
    "        sel_exam = sel_exam.drop_duplicates(subset=['Domain'], keep='first')\n",
    "        \n",
    "        # calculate percentages\n",
    "        sel_exam['count_pct'] = sel_exam['Domain_freq'].apply(lambda x: x/sum(sel_exam['Domain_freq']))\n",
    "        \n",
    "        # sort descending\n",
    "        sel_exam=sel_exam.sort_values(by=['count_pct'],ascending=False).reset_index()\n",
    "        \n",
    "        # plot on subplots \n",
    "        ax[i].bar(x=sel_exam['Domain'].values,height=sel_exam['count_pct'].values,color=color[i])\n",
    "        ax[i].set_title(f'{date} Domain Percentages',fontsize=30)\n",
    "        ax[i].tick_params(axis='both', which='major', labelsize=20)\n",
    "        \n",
    "        \n",
    "# sub plot adjustments\n",
    "f.subplots_adjust(top=.99, bottom=0.01, wspace=0.2,hspace=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# left off 10:00pm on 7/29/18"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary\n",
    "#### Answers to the questions above will be summarized here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Is the frequency of each cluster of questions consistent through exam?\n",
    "2. Does the frequency of each cluster hold true with the engageny guidelines?\n",
    "3. Are there clusters being skipped? If so why and is there consistence with those omissions?\n",
    "4. Which clusters in a domain are more widely assessed?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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