docs/math2015/Math1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "consolidated-potato",
   "metadata": {},
   "source": [
    "# math2015-Math1 Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "greenhouse-sphere",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import plotly.express as px\n",
    "from plotly.subplots import make_subplots\n",
    "import plotly.graph_objs as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "green-backup",
   "metadata": {},
   "outputs": [],
   "source": [
    "path = \"C:/Users/Administrator/Desktop/Math1/rawdata.txt\"\n",
    "data = pd.read_table(path,header=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unlikely-compression",
   "metadata": {},
   "source": [
    "## RECORDS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "imported-consensus",
   "metadata": {},
   "source": [
    "The learning records are saved in a score matrix. Each row corresponds to the records of a student on different test items."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "impossible-simple",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "<p>4209 rows × 20 columns</p>\n",
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      "text/plain": [
       "      0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  \\\n",
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       "2      4   4   0   0   0   0   4   0   0   4   0   4   0   0   0   0   0   0   \n",
       "3      4   4   4   0   0   0   4   4   4   0   4   4   4   4   0   5   0   0   \n",
       "4      0   4   4   0   4   0   4   0   0   0   4   4   0   4   0   3   0   0   \n",
       "...   ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..   \n",
       "4204   4   0   4   4   4   0   4   0   0   4   0   0   0   0   0   4   2   0   \n",
       "4205   0   4   4   0   4   4   4   0   0   0   0   0   0   0   0   3   0   0   \n",
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       "4207   4   0   4   4   0   4   0   0   4   0   0   4   0   4   0   4   1   2   \n",
       "4208   4   0   4   0   4   0   0   4   0   0   0   4   0   0   0   3   0   0   \n",
       "\n",
       "      18  19  \n",
       "0      5   4  \n",
       "1      2   0  \n",
       "2      0   0  \n",
       "3      0   0  \n",
       "4      0   0  \n",
       "...   ..  ..  \n",
       "4204   1   0  \n",
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       "4208   1   0  \n",
       "\n",
       "[4209 rows x 20 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.set_option('display.max_rows',10)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hydraulic-promotion",
   "metadata": {},
   "source": [
    "For example, the first row presents the learning records of student 0 where he gets 4 point on item 0 and 5 point on item 18. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "attached-maldives",
   "metadata": {},
   "source": [
    "## General features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "front-pillow",
   "metadata": {},
   "outputs": [
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>9.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0            1            2            3            4   \\\n",
       "count  4209.000000  4209.000000  4209.000000  4209.000000  4209.000000   \n",
       "mean      2.983131     2.421478     2.532668     2.827275     2.205750   \n",
       "std       1.741888     1.955317     1.927991     1.821100     1.989625   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "50%       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "75%       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "max       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "\n",
       "                5            6            7            8            9   \\\n",
       "count  4209.000000  4209.000000  4209.000000  4209.000000  4209.000000   \n",
       "mean      2.109765     3.573295     2.387265     1.588976     1.663103   \n",
       "std       1.997223     1.234951     1.962381     1.957542     1.971655   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     4.000000     0.000000     0.000000     0.000000   \n",
       "50%       4.000000     4.000000     4.000000     0.000000     0.000000   \n",
       "75%       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "max       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "\n",
       "                10           11           12           13           14  \\\n",
       "count  4209.000000  4209.000000  4209.000000  4209.000000  4209.000000   \n",
       "mean      2.438584     2.986933     1.044429     2.305536     0.022808   \n",
       "std       1.951550     1.739736     1.757162     1.976759     0.301222   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "50%       4.000000     4.000000     0.000000     4.000000     0.000000   \n",
       "75%       4.000000     4.000000     4.000000     4.000000     0.000000   \n",
       "max       4.000000     4.000000     4.000000     4.000000     4.000000   \n",
       "\n",
       "                15           16           17           18           19  \n",
       "count  4209.000000  4209.000000  4209.000000  4209.000000  4209.000000  \n",
       "mean      4.247327     2.692564     1.226657     2.333333     0.953196  \n",
       "std       1.476007     2.789518     2.238923     2.110050     1.378800  \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  \n",
       "25%       3.000000     0.000000     0.000000     1.000000     0.000000  \n",
       "50%       5.000000     2.000000     0.000000     2.000000     0.000000  \n",
       "75%       5.000000     4.000000     1.000000     4.000000     2.000000  \n",
       "max       6.000000     8.000000     8.000000     9.000000     9.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "powered-mistake",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of records:4209\n"
     ]
    }
   ],
   "source": [
    "print('The number of records:' + str(len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "standing-speaker",
   "metadata": {},
   "outputs": [
    {
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font-size: 17px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">Top 50 students by score</text></g><g class=\"g-xtitle\"><text class=\"xtitle\" x=\"350\" y=\"410.20625\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">count</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,18.231250000000003,235)\" x=\"18.231250000000003\" y=\"235\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">index1</text></g></g></svg>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['count']=data.apply(lambda x: x.sum(),axis=1)\n",
    "data['index1']=data.index\n",
    "ds=data.loc[:, ['count', 'index1']]\n",
    "ds['index1'] = ds['index1'].astype(str) + '-'\n",
    "ds = ds.sort_values(['count']).tail(50)\n",
    "fig = px.bar(\n",
    "    ds,\n",
    "    x = 'count',\n",
    "    y = 'index1',\n",
    "    orientation='h',\n",
    "    title='Top 50 students by score'\n",
    ")\n",
    "\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "digital-discipline",
   "metadata": {},
   "source": [
    "This figure shows the total score of Top 50 students."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "general-uruguay",
   "metadata": {},
   "outputs": [
    {
     "data": {
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white-space: pre;\">index1</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,23.684375000000003,235)\" x=\"23.684375000000003\" y=\"235\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">sum of count</text></g></g></svg>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds=data.loc[:, ['count', 'index1']]\n",
    "ds = ds.sort_values(['index1'])\n",
    "fig = px.histogram(\n",
    "    ds,\n",
    "    x='index1',\n",
    "    y='count',\n",
    "    title='Students score distribution'\n",
    ")\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "gothic-bradford",
   "metadata": {},
   "source": [
    "## Sort by correct rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ordinary-apollo",
   "metadata": {},
   "outputs": [],
   "source": [
    "path = \"C:/Users/Administrator/Desktop/Math1/data.txt\"\n",
    "data = pd.read_table(path,header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "peaceful-archives",
   "metadata": {},
   "outputs": [
    {
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font-size: 14px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">count</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,33.48125,235)\" x=\"33.48125\" y=\"235\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">problem_id</text></g></g></svg>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds = data.mean()\n",
    "ds1=pd.DataFrame(columns=['problem_id','count'])\n",
    "for i in range(len(ds)):\n",
    "    new=pd.DataFrame({\n",
    "        'problem_id':int(i),\n",
    "        'count':ds[i]\n",
    "    },index=[0]\n",
    "    )\n",
    "    ds1=ds1.append(new,ignore_index=True)\n",
    "\n",
    "ds1=ds1.sort_values(['count'])\n",
    "ds1['problem_id'] = (ds1['problem_id']).astype(str) + '-'\n",
    "fig = px.bar(\n",
    "    ds1,\n",
    "    x = 'count',\n",
    "    y = 'problem_id',\n",
    "    orientation = 'h',\n",
    "    title = 'Average correct rate of questions'\n",
    ")\n",
    "\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "greek-crash",
   "metadata": {},
   "source": [
    "This figure presents the average correct rate of questions.It's obvious that students do the best on item 6 but need to improve on item 14."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "electric-vessel",
   "metadata": {},
   "source": [
    "## Sort by problem type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "early-practitioner",
   "metadata": {},
   "outputs": [
    {
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font-size: 17px; fill: rgb(42, 63, 95); opacity: 1; font-weight: normal; white-space: pre;\">Average correct rate of questions for every problem type</text></g><g class=\"g-xtitle\"/><g class=\"g-x2title\"/><g class=\"g-ytitle\"/><g class=\"g-y2title\"/></g></svg>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds = data.mean()\n",
    "ds1=pd.DataFrame(columns=['problem_id','count'])\n",
    "for i in range(len(ds)):\n",
    "    new=pd.DataFrame({\n",
    "        'problem_id':int(i),\n",
    "        'count':ds[i]\n",
    "    },index=[0]\n",
    "    )\n",
    "    ds1=ds1.append(new,ignore_index=True)\n",
    "\n",
    "data2= [('Obj',ds1[ds1['problem_id']<15]['count'].mean()),\n",
    "    ('Sub',ds1[ds1['problem_id']>=14]['count'].mean())]\n",
    "ds2 = pd.DataFrame(\n",
    "    data=data2,\n",
    "    columns=['Type','Percent']\n",
    ")\n",
    "\n",
    "fig = make_subplots(rows=1,cols=2)\n",
    "traces = [\n",
    "    go.Bar(\n",
    "        x=['wrong','right'],\n",
    "        y=[ \n",
    "        1-float(ds2[ds2['Type']==item]['Percent']),\n",
    "        float(ds2[ds2['Type']==item]['Percent'])\n",
    "        ],\n",
    "        name='Type:' + str(item),\n",
    "        text=[\n",
    "        str(round(100*(1-float(ds2[ds2['Type']==item]['Percent'])))) + '%',\n",
    "        str(round(100*float(ds2[ds2['Type']==item]['Percent']))) + '%'\n",
    "        ],\n",
    "        textposition='auto'\n",
    "    ) for item in ds2['Type'].tolist()\n",
    "]\n",
    "for i in range(len(traces)):\n",
    "    fig.append_trace(\n",
    "        traces[i],\n",
    "        (i //2) + 1,\n",
    "        (i % 2) + 1\n",
    "    )    \n",
    "fig.update_layout(\n",
    "    title_text = 'Average correct rate of questions for every problem type',\n",
    ")\n",
    "\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "occasional-exception",
   "metadata": {},
   "source": [
    "This figure shows that students do better in objective questions but there is a huge gap in the average correct rate of subjective and objective questions. The subjective questions are a challenge to students and their ability to answer them needs to be strengthened."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "heard-reynolds",
   "metadata": {},
   "outputs": [],
   "source": [
    "path = \"C:/Users/Administrator/Desktop/Math1/problemdesc.txt\"\n",
    "data1 = pd.read_table(path,header=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "outer-angel",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count = data1['Full Score'].sum()\n",
    "data2= [('Obj',data1[data1['Type']=='Obj']['Full Score'].sum()),\n",
    "    ('Sub',data1[data1['Type']=='Sub']['Full Score'].sum())]\n",
    "ds = pd.DataFrame(\n",
    "    data=data2,\n",
    "    columns=['Type','Percent']\n",
    ")\n",
    "\n",
    "ds['Percent']/=count\n",
    "ds=ds.sort_values('Percent')\n",
    "\n",
    "fig=px.pie(\n",
    "    ds,\n",
    "    names='Type',\n",
    "    values='Percent',\n",
    "    title='Problem type',\n",
    ")\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "impaired-letters",
   "metadata": {},
   "source": [
    "## Sort by skills"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "protective-monthly",
   "metadata": {},
   "outputs": [],
   "source": [
    "path1 = \"C:/Users/Administrator/Desktop/Math1/q.txt\"\n",
    "data1 = pd.read_table(path1,header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "vietnamese-arthritis",
   "metadata": {},
   "outputs": [],
   "source": [
    "ds1 = data1.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "insured-abortion",
   "metadata": {},
   "outputs": [],
   "source": [
    "path2 = \"C:/Users/Administrator/Desktop/Math1/qnames.txt\"\n",
    "data2 = pd.read_table(path2,header=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "detailed-shadow",
   "metadata": {},
   "outputs": [],
   "source": [
    "ds=pd.DataFrame(columns=['skill','count'])\n",
    "for i in range(len(ds1)):\n",
    "    new=pd.DataFrame({ \n",
    "        'skill':data2['Skill Names'][i],\n",
    "        'count':ds1[i]\n",
    "    },index=[0]\n",
    "    )\n",
    "    ds=ds.append(new,ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "royal-planner",
   "metadata": {},
   "outputs": [
    {
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     "metadata": {},
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    }
   ],
   "source": [
    "ds=ds.sort_values(['count'])\n",
    "fig = px.bar(\n",
    "    ds,\n",
    "    x='count',\n",
    "    y='skill',\n",
    "    orientation='h',\n",
    "    title='Skill count'\n",
    ")\n",
    "fig.show(\"svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "impressive-leonard",
   "metadata": {},
   "source": [
    "This figure shows that calculation is the most important skill in the test as almost every item is related to it. Besides, reasoning and demonstration is also the key to do better in the test."
   ]
  }
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