第6章缺失数据.ipynb · OnlyGenius/pandas 学习

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第6章缺失数据.ipynb 168.88 KB

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第6章 缺失数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 在接下来的两章中，会接触到数据预处理中比较麻烦的类型，即缺失数据和文本数据（尤其是混杂型文本）\n",
    "#### Pandas在步入1.0后，对数据类型也做出了新的尝试，尤其是Nullable类型和String类型，了解这些可能在未来成为主流的新特性是必要的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>School</th>\n",
       "      <th>Class</th>\n",
       "      <th>ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Address</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Math</th>\n",
       "      <th>Physics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>S_1</td>\n",
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       "      <td>street_1</td>\n",
       "      <td>173</td>\n",
       "      <td>NaN</td>\n",
       "      <td>34.0</td>\n",
       "      <td>A+</td>\n",
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       "      <td>S_1</td>\n",
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       "      <td>street_2</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>32.5</td>\n",
       "      <td>B+</td>\n",
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       "      <th>2</th>\n",
       "      <td>S_1</td>\n",
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       "      <td>1103.0</td>\n",
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       "      <th>3</th>\n",
       "      <td>S_1</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>167</td>\n",
       "      <td>81.0</td>\n",
       "      <td>80.4</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>S_1</td>\n",
       "      <td>C_1</td>\n",
       "      <td>1105.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>street_4</td>\n",
       "      <td>159</td>\n",
       "      <td>64.0</td>\n",
       "      <td>84.8</td>\n",
       "      <td>A-</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  School Class      ID Gender   Address  Height  Weight  Math Physics\n",
       "0    S_1   C_1     NaN      M  street_1     173     NaN  34.0      A+\n",
       "1    S_1   C_1     NaN      F  street_2     192     NaN  32.5      B+\n",
       "2    S_1   C_1  1103.0      M  street_2     186     NaN  87.2      B+\n",
       "3    S_1   NaN     NaN      F  street_2     167    81.0  80.4     NaN\n",
       "4    S_1   C_1  1105.0    NaN  street_4     159    64.0  84.8      A-"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "df = pd.read_csv('data/table_missing.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 一、缺失观测及其类型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 了解缺失信息\n",
    "#### （a）isna和notna方法\n",
    "#### 对Series使用会返回布尔列表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2    False\n",
       "3     True\n",
       "4    False\n",
       "Name: Physics, dtype: bool"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Physics'].isna().head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     True\n",
       "1     True\n",
       "2     True\n",
       "3    False\n",
       "4     True\n",
       "Name: Physics, dtype: bool"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Physics'].notna().head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 对DataFrame使用会返回布尔表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>School</th>\n",
       "      <th>Class</th>\n",
       "      <th>ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Address</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Math</th>\n",
       "      <th>Physics</th>\n",
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       "      <th>1</th>\n",
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       "      <th>3</th>\n",
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       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   School  Class     ID  Gender  Address  Height  Weight   Math  Physics\n",
       "0   False  False   True   False    False   False    True  False    False\n",
       "1   False  False   True   False    False   False    True  False    False\n",
       "2   False  False  False   False    False   False    True  False    False\n",
       "3   False   True   True   False    False   False   False  False     True\n",
       "4   False  False  False    True    False   False   False  False    False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 但对于DataFrame我们更关心到底每列有多少缺失值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "School      0\n",
       "Class       4\n",
       "ID          6\n",
       "Gender      7\n",
       "Address     0\n",
       "Height      0\n",
       "Weight     13\n",
       "Math        5\n",
       "Physics     4\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 此外，可以通过第1章中介绍的info函数查看缺失信息"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 35 entries, 0 to 34\n",
      "Data columns (total 9 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   School   35 non-null     object \n",
      " 1   Class    31 non-null     object \n",
      " 2   ID       29 non-null     float64\n",
      " 3   Gender   28 non-null     object \n",
      " 4   Address  35 non-null     object \n",
      " 5   Height   35 non-null     int64  \n",
      " 6   Weight   22 non-null     float64\n",
      " 7   Math     30 non-null     float64\n",
      " 8   Physics  31 non-null     object \n",
      "dtypes: float64(3), int64(1), object(5)\n",
      "memory usage: 2.6+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）查看缺失值的所以在行"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 以最后一列为例，挑出该列缺失值的行"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "      <th>8</th>\n",
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       "      <td>63.0</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>S_1</td>\n",
       "      <td>C_3</td>\n",
       "      <td>1304.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>street_2</td>\n",
       "      <td>195</td>\n",
       "      <td>70.0</td>\n",
       "      <td>85.2</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_2</td>\n",
       "      <td>2203.0</td>\n",
       "      <td>M</td>\n",
       "      <td>street_4</td>\n",
       "      <td>155</td>\n",
       "      <td>91.0</td>\n",
       "      <td>73.8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   School Class      ID Gender   Address  Height  Weight  Math Physics\n",
       "3     S_1   NaN     NaN      F  street_2     167    81.0  80.4     NaN\n",
       "8     S_1   C_2  1204.0      F  street_5     162    63.0  33.8     NaN\n",
       "13    S_1   C_3  1304.0    NaN  street_2     195    70.0  85.2     NaN\n",
       "22    S_2   C_2  2203.0      M  street_4     155    91.0  73.8     NaN"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df['Physics'].isna()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （c）挑选出所有非缺失值列\n",
    "#### 使用all就是全部非缺失值，如果是any就是至少有一个不是缺失值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <th>5</th>\n",
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       "      <td>97.0</td>\n",
       "      <td>A-</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>S_1</td>\n",
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       "      <td>94.0</td>\n",
       "      <td>63.5</td>\n",
       "      <td>B-</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>S_1</td>\n",
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       "      <td>1303.0</td>\n",
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       "      <td>188</td>\n",
       "      <td>82.0</td>\n",
       "      <td>49.7</td>\n",
       "      <td>B</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_1</td>\n",
       "      <td>2103.0</td>\n",
       "      <td>M</td>\n",
       "      <td>street_4</td>\n",
       "      <td>157</td>\n",
       "      <td>61.0</td>\n",
       "      <td>52.5</td>\n",
       "      <td>B-</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_2</td>\n",
       "      <td>2202.0</td>\n",
       "      <td>F</td>\n",
       "      <td>street_7</td>\n",
       "      <td>194</td>\n",
       "      <td>77.0</td>\n",
       "      <td>68.5</td>\n",
       "      <td>B+</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_3</td>\n",
       "      <td>2301.0</td>\n",
       "      <td>F</td>\n",
       "      <td>street_4</td>\n",
       "      <td>157</td>\n",
       "      <td>78.0</td>\n",
       "      <td>72.3</td>\n",
       "      <td>B+</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_3</td>\n",
       "      <td>2303.0</td>\n",
       "      <td>F</td>\n",
       "      <td>street_7</td>\n",
       "      <td>190</td>\n",
       "      <td>99.0</td>\n",
       "      <td>65.9</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_3</td>\n",
       "      <td>2304.0</td>\n",
       "      <td>F</td>\n",
       "      <td>street_6</td>\n",
       "      <td>164</td>\n",
       "      <td>81.0</td>\n",
       "      <td>95.5</td>\n",
       "      <td>A-</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>S_2</td>\n",
       "      <td>C_3</td>\n",
       "      <td>2305.0</td>\n",
       "      <td>M</td>\n",
       "      <td>street_4</td>\n",
       "      <td>187</td>\n",
       "      <td>73.0</td>\n",
       "      <td>48.9</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   School Class      ID Gender   Address  Height  Weight  Math Physics\n",
       "5     S_1   C_2  1201.0      M  street_5     159    68.0  97.0      A-\n",
       "6     S_1   C_2  1202.0      F  street_4     176    94.0  63.5      B-\n",
       "12    S_1   C_3  1303.0      M  street_7     188    82.0  49.7       B\n",
       "17    S_2   C_1  2103.0      M  street_4     157    61.0  52.5      B-\n",
       "21    S_2   C_2  2202.0      F  street_7     194    77.0  68.5      B+\n",
       "25    S_2   C_3  2301.0      F  street_4     157    78.0  72.3      B+\n",
       "27    S_2   C_3  2303.0      F  street_7     190    99.0  65.9       C\n",
       "28    S_2   C_3  2304.0      F  street_6     164    81.0  95.5      A-\n",
       "29    S_2   C_3  2305.0      M  street_4     187    73.0  48.9       B"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.notna().all(1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 三种缺失符号\n",
    "#### （a）np.nan\n",
    "#### np.nan是一个麻烦的东西，首先它不等与任何东西，甚至不等于自己"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nan == np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nan == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.nan == None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 在用equals函数比较时，自动略过两侧全是np.nan的单元格，因此结果不会影响"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.equals(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 其次，它在numpy中的类型为浮点，由此导致数据集读入时，即使原来是整数的列，只要有缺失值就会变为浮点型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(np.nan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([1,2,3]).dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([1,np.nan,3]).dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 此外，对于布尔类型的列表，如果是np.nan填充，那么它的值会自动变为True而不是False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    True\n",
       "1    True\n",
       "2    True\n",
       "dtype: bool"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([1,np.nan,3],dtype='bool')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 但当修改一个布尔列表时，会改变列表类型，而不是赋值为True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([True,False],dtype='bool')\n",
    "s[1]=np.nan\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 在所有的表格读取后，无论列是存放什么类型的数据，默认的缺失值全为np.nan类型\n",
    "#### 因此整型列转为浮点；而字符由于无法转化为浮点，因此只能归并为object类型（'O'），原来是浮点型的则类型不变"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['ID'].dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Math'].dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('O')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Class'].dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）None\n",
    "#### None比前者稍微好些，至少它会等于自身"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "None == None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 它的布尔值为False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([None],dtype='bool')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 修改布尔列表不会改变数据类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([True,False],dtype='bool')\n",
    "s[0]=None\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([1,0],dtype='bool')\n",
    "s[0]=None\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 在传入数值类型后，会自动变为np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(pd.Series([1,None])[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 只有当传入object类型是保持不动，几乎可以认为，除非人工命名None，它基本不会自动出现在Pandas中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NoneType"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(pd.Series([1,None],dtype='O')[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  在使用equals函数时不会被略过，因此下面的情况下返回False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([None]).equals(pd.Series([np.nan]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （c）NaT\n",
    "#### NaT是针对时间序列的缺失值，是Pandas的内置类型，可以完全看做时序版本的np.nan，与自己不等，且使用equals是也会被跳过"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   2012-01-01\n",
       "1   2012-01-01\n",
       "2   2012-01-01\n",
       "3   2012-01-01\n",
       "4   2012-01-01\n",
       "dtype: datetime64[ns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time = pd.Series([pd.Timestamp('20120101')]*5)\n",
    "s_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   2012-01-01\n",
       "1   2012-01-01\n",
       "2          NaT\n",
       "3   2012-01-01\n",
       "4   2012-01-01\n",
       "dtype: datetime64[ns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time[2] = None\n",
    "s_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   2012-01-01\n",
       "1   2012-01-01\n",
       "2          NaT\n",
       "3   2012-01-01\n",
       "4   2012-01-01\n",
       "dtype: datetime64[ns]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time[2] = np.nan\n",
    "s_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   2012-01-01\n",
       "1   2012-01-01\n",
       "2          NaT\n",
       "3   2012-01-01\n",
       "4   2012-01-01\n",
       "dtype: datetime64[ns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time[2] = pd.NaT\n",
    "s_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas._libs.tslibs.nattype.NaTType"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(s_time[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time[2] == s_time[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_time.equals(s_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    True\n",
       "1    True\n",
       "dtype: bool"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([True,False],dtype='bool')\n",
    "s[1]=pd.NaT\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Nullable类型与NA符号\n",
    "#### 这是Pandas在1.0新版本中引入的重大改变，其目的就是为了（在若干版本后）解决之前出现的混乱局面，统一缺失值处理方法\n",
    "#### \"The goal of pd.NA is provide a “missing” indicator that can be used consistently across data types (instead of np.nan, None or pd.NaT depending on the data type).\"——User Guide for Pandas v-1.0\n",
    "#### 官方鼓励用户使用新的数据类型和缺失类型pd.NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （a）Nullable整形\n",
    "#### 对于该种类型而言，它与原来标记int上的符号区别在于首字母大写：'Int'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_original = pd.Series([1, 2], dtype=\"int64\")\n",
    "s_original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    2\n",
       "dtype: Int64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new = pd.Series([1, 2], dtype=\"Int64\")\n",
    "s_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 它的好处就在于，其中前面提到的三种缺失值都会被替换为统一的NA符号，且不改变数据类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_original[1] = np.nan\n",
    "s_original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       1\n",
       "1    <NA>\n",
       "dtype: Int64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[1] = np.nan\n",
    "s_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       1\n",
       "1    <NA>\n",
       "dtype: Int64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[1] = None\n",
    "s_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       1\n",
       "1    <NA>\n",
       "dtype: Int64"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[1] = pd.NaT\n",
    "s_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）Nullable布尔\n",
    "#### 对于该种类型而言，作用与上面的类似，记号为boolean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     True\n",
       "1    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_original = pd.Series([1, 0], dtype=\"bool\")\n",
    "s_original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     True\n",
       "dtype: boolean"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new = pd.Series([0, 1], dtype=\"boolean\")\n",
    "s_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    NaN\n",
       "1    0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_original[0] = np.nan\n",
    "s_original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_original = pd.Series([1, 0], dtype=\"bool\") #此处重新加一句是因为前面赋值改变了bool类型\n",
    "s_original[0] = None\n",
    "s_original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1    True\n",
       "dtype: boolean"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[0] = np.nan\n",
    "s_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1    True\n",
       "dtype: boolean"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[0] = None\n",
    "s_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1    True\n",
       "dtype: boolean"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_new[0] = pd.NaT\n",
    "s_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 需要注意的是，含有pd.NA的布尔列表在1.0.2之前的版本作为索引时会报错，这是一个之前的[bug](https://pandas.pydata.org/docs/whatsnew/v1.0.2.html#indexing-with-nullable-boolean-arrays)，现已经修复"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    cat\n",
       "dtype: object"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series(['dog','cat'])\n",
    "s[s_new]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （c）string类型\n",
    "#### 该类型是1.0的一大创新，目的之一就是为了区分开原本含糊不清的object类型，这里将简要地提及string，因为它是第7章的主题内容\n",
    "#### 它本质上也属于Nullable类型，因为并不会因为含有缺失而改变类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    dog\n",
       "1    cat\n",
       "dtype: string"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series(['dog','cat'],dtype='string')\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1     cat\n",
       "dtype: string"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[0] = np.nan\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1     cat\n",
       "dtype: string"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[0] = None\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    <NA>\n",
       "1     cat\n",
       "dtype: string"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[0] = pd.NaT\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 此外，和object类型的一点重要区别就在于，在调用字符方法后，string类型返回的是Nullable类型，object则会根据缺失类型和数据类型而改变"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       1\n",
       "1    <NA>\n",
       "2       0\n",
       "dtype: Int64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([\"a\", None, \"b\"], dtype=\"string\")\n",
    "s.str.count('a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    NaN\n",
       "2    0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 = pd.Series([\"a\", None, \"b\"], dtype=\"object\")\n",
    "s2.str.count(\"a\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     <NA>\n",
       "2    False\n",
       "dtype: boolean"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.str.isdigit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1     None\n",
       "2    False\n",
       "dtype: object"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2.str.isdigit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. NA的特性"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （a）逻辑运算\n",
    "#### 只需看该逻辑运算的结果是否依赖pd.NA的取值，如果依赖，则结果还是NA，如果不依赖，则直接计算结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True | pd.NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.NA | True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False | pd.NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False & pd.NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True & pd.NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 取值不明直接报错"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "#bool(pd.NA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）算术运算和比较运算\n",
    "#### 这里只需记住除了下面两类情况，其他结果都是NA即可"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.NA ** 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 ** pd.NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 其他情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.NA + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"a\" * pd.NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.NA == pd.NA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.NA < 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(pd.NA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<NA>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(pd.NA, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.  convert_dtypes方法\n",
    "#### 这个函数的功能往往就是在读取数据时，就把数据列转为Nullable类型，是1.0的新函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "School      object\n",
       "Class       object\n",
       "ID         float64\n",
       "Gender      object\n",
       "Address     object\n",
       "Height       int64\n",
       "Weight     float64\n",
       "Math       float64\n",
       "Physics     object\n",
       "dtype: object"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.read_csv('data/table_missing.csv').dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "School      string\n",
       "Class       string\n",
       "ID           Int64\n",
       "Gender      string\n",
       "Address     string\n",
       "Height       Int64\n",
       "Weight       Int64\n",
       "Math       float64\n",
       "Physics     string\n",
       "dtype: object"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.read_csv('data/table_missing.csv').convert_dtypes().dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二、缺失数据的运算与分组"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 加号与乘号规则"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 使用加法时，缺失值为0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([2,3,np.nan,4])\n",
    "s.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 使用乘法时，缺失值为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.0"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.prod()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 使用累计函数时，缺失值自动略过"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2.0\n",
       "1    5.0\n",
       "2    NaN\n",
       "3    9.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     2.0\n",
       "1     6.0\n",
       "2     NaN\n",
       "3    24.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.cumprod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         NaN\n",
       "1    0.500000\n",
       "2    0.000000\n",
       "3    0.333333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.pct_change()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. groupby方法中的缺失值\n",
    "#### 自动忽略为缺失值的组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>-1.126645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>B</td>\n",
       "      <td>0.924595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>C</td>\n",
       "      <td>-2.076309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>D</td>\n",
       "      <td>-0.312150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.961543</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   one       two\n",
       "0    A -1.126645\n",
       "1    B  0.924595\n",
       "2    C -2.076309\n",
       "3    D -0.312150\n",
       "4  NaN  0.961543"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_g = pd.DataFrame({'one':['A','B','C','D',np.nan],'two':np.random.randn(5)})\n",
    "df_g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': Int64Index([0], dtype='int64'),\n",
       " 'B': Int64Index([1], dtype='int64'),\n",
       " 'C': Int64Index([2], dtype='int64'),\n",
       " 'D': Int64Index([3], dtype='int64')}"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_g.groupby('one').groups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 三、填充与剔除"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. fillna方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （a）值填充与前后向填充（分别与ffill方法和bfill方法等价）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         A+\n",
       "1         B+\n",
       "2         B+\n",
       "3    missing\n",
       "4         A-\n",
       "Name: Physics, dtype: object"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Physics'].fillna('missing').head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    A+\n",
       "1    B+\n",
       "2    B+\n",
       "3    B+\n",
       "4    A-\n",
       "Name: Physics, dtype: object"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Physics'].fillna(method='ffill').head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    A+\n",
       "1    B+\n",
       "2    B+\n",
       "3    A-\n",
       "4    A-\n",
       "Name: Physics, dtype: object"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Physics'].fillna(method='backfill').head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）填充中的对齐特性"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
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       "</table>\n",
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      "text/plain": [
       "     A    B    C\n",
       "0  1.0  2.0  3.0\n",
       "1  3.0  4.0  5.0\n",
       "2  2.0  3.0  4.0"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_f = pd.DataFrame({'A':[1,3,np.nan],'B':[2,4,np.nan],'C':[3,5,np.nan]})\n",
    "df_f.fillna(df_f.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 返回的结果中没有C，根据对齐特点不会被填充"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "      <th>C</th>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A    B    C\n",
       "0  1.0  2.0  3.0\n",
       "1  3.0  4.0  5.0\n",
       "2  2.0  3.0  NaN"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_f.fillna(df_f.mean()[['A','B']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. dropna方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （a）axis参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    A    B  C\n",
       "0 NaN  NaN  3\n",
       "1 NaN  3.0  2\n",
       "2 NaN  2.0  1"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_d = pd.DataFrame({'A':[np.nan,np.nan,np.nan],'B':[np.nan,3,2],'C':[3,2,1]})\n",
    "df_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [A, B, C]\n",
       "Index: []"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_d.dropna(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   C\n",
       "0  3\n",
       "1  2\n",
       "2  1"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_d.dropna(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）how参数（可以选all或者any，表示全为缺失去除和存在缺失去除）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     B  C\n",
       "0  NaN  3\n",
       "1  3.0  2\n",
       "2  2.0  1"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_d.dropna(axis=1,how='all')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （c）subset参数（即在某一组列范围中搜索缺失值）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    A    B  C\n",
       "1 NaN  3.0  2\n",
       "2 NaN  2.0  1"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_d.dropna(axis=0,subset=['B','C'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 四、插值（interpolation）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 线性插值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （a）索引无关的线性插值\n",
    "#### 默认状态下，interpolate会对缺失的值进行线性插值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     1.0\n",
       "1    10.0\n",
       "2    15.0\n",
       "3    -5.0\n",
       "4    -2.0\n",
       "5     NaN\n",
       "6     NaN\n",
       "7    28.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([1,10,15,-5,-2,np.nan,np.nan,28])\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     1.0\n",
       "1    10.0\n",
       "2    15.0\n",
       "3    -5.0\n",
       "4    -2.0\n",
       "5     8.0\n",
       "6    18.0\n",
       "7    28.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.interpolate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7df20af50>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "s.interpolate().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 此时的插值与索引无关"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69      1.0\n",
       "71     10.0\n",
       "84     15.0\n",
       "117    -5.0\n",
       "119    -2.0\n",
       "171     8.0\n",
       "219    18.0\n",
       "236    28.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.index = np.sort(np.random.randint(50,300,8))\n",
    "s.interpolate()\n",
    "#值不变"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7dfc69890>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "s.interpolate().plot()\n",
    "#后面三个点不是线性的（如果几乎为线性函数，请重新运行上面的一个代码块，这是随机性导致的）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）与索引有关的插值\n",
    "#### method中的index和time选项可以使插值线性地依赖索引，即插值为索引的线性函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7dca0c4d0>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "s.interpolate(method='index').plot()\n",
    "#可以看到与上面的区别"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 如果索引是时间，那么可以按照时间长短插值，对于时间序列将在第9章详细介绍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-05-01     0.0\n",
       "2012-05-07     NaN\n",
       "2012-06-03    10.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_t = pd.Series([0,np.nan,10]\n",
    "        ,index=[pd.Timestamp('2012-05-01'),pd.Timestamp('2012-05-07'),pd.Timestamp('2012-06-03')])\n",
    "s_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7dc964850>"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "s_t.interpolate().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7dc8eda10>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "s_t.interpolate(method='time').plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 高级插值方法\n",
    "#### 此处的高级指的是与线性插值相比较，例如样条插值、多项式插值、阿基玛插值等（需要安装Scipy），方法详情请看[这里](https://pandas.pydata.org/pandas-docs/version/1.0.0/reference/api/pandas.DataFrame.interpolate.html#pandas.DataFrame.interpolate)\n",
    "#### 关于这部分仅给出一个官方的例子，因为插值方法是数值分析的内容，而不是Pandas中的基本知识："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe7dc86f810>"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "ser = pd.Series(np.arange(1, 10.1, .25) ** 2 + np.random.randn(37))\n",
    "missing = np.array([4, 13, 14, 15, 16, 17, 18, 20, 29])\n",
    "ser[missing] = np.nan\n",
    "methods = ['linear', 'quadratic', 'cubic']\n",
    "df = pd.DataFrame({m: ser.interpolate(method=m) for m in methods})\n",
    "df.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. interpolate中的限制参数\n",
    "#### （a）limit表示最多插入多少个"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    2.0\n",
       "2    3.0\n",
       "3    NaN\n",
       "4    5.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([1,np.nan,np.nan,np.nan,5])\n",
    "s.interpolate(limit=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （b）limit_direction表示插值方向，可选forward,backward,both，默认前向"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    1.0\n",
       "2    1.0\n",
       "3    2.0\n",
       "4    3.0\n",
       "5    4.0\n",
       "6    5.0\n",
       "7    NaN\n",
       "8    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([np.nan,np.nan,1,np.nan,np.nan,np.nan,5,np.nan,np.nan,])\n",
    "s.interpolate(limit_direction='backward')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### （c）limit_area表示插值区域，可选inside,outside，默认None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    NaN\n",
       "1    NaN\n",
       "2    1.0\n",
       "3    2.0\n",
       "4    3.0\n",
       "5    4.0\n",
       "6    5.0\n",
       "7    NaN\n",
       "8    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([np.nan,np.nan,1,np.nan,np.nan,np.nan,5,np.nan,np.nan,])\n",
    "s.interpolate(limit_area='inside')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    NaN\n",
       "1    NaN\n",
       "2    1.0\n",
       "3    NaN\n",
       "4    NaN\n",
       "5    NaN\n",
       "6    5.0\n",
       "7    5.0\n",
       "8    5.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([np.nan,np.nan,1,np.nan,np.nan,np.nan,5,np.nan,np.nan,])\n",
    "s.interpolate(limit_area='outside')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 五、问题与练习"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 【问题一】 如何删除缺失值占比超过25%的列？\n",
    "#### 【问题二】 什么是Nullable类型？请谈谈为什么要引入这个设计？\n",
    "#### 【问题三】 对于一份有缺失值的数据，可以采取哪些策略或方法深化对它的了解？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 练习"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 【练习一】现有一份虚拟数据集，列类型分别为string/浮点/整型，请解决如下问题：\n",
    "#### （a）请以列类型读入数据，并选出C为缺失值的行。\n",
    "#### （b）现需要将A中的部分单元转为缺失值，单元格中的最小转换概率为25%，且概率大小与所在行B列单元的值成正比。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>not_NaN</td>\n",
       "      <td>0.922</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>not_NaN</td>\n",
       "      <td>0.700</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>not_NaN</td>\n",
       "      <td>0.503</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>not_NaN</td>\n",
       "      <td>0.938</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>not_NaN</td>\n",
       "      <td>0.952</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         A      B     C\n",
       "0  not_NaN  0.922   4.0\n",
       "1  not_NaN  0.700   NaN\n",
       "2  not_NaN  0.503   8.0\n",
       "3  not_NaN  0.938   4.0\n",
       "4  not_NaN  0.952  10.0"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.read_csv('data/Missing_data_one.csv').head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 【练习二】 现有一份缺失的数据集，记录了36个人来自的地区、身高、体重、年龄和工资，请解决如下问题：\n",
    "#### （a）统计各列缺失的比例并选出在后三列中至少有两个非缺失值的行。\n",
    "#### （b）请结合身高列和地区列中的数据，对体重进行合理插值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "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>编号</th>\n",
       "      <th>地区</th>\n",
       "      <th>身高</th>\n",
       "      <th>体重</th>\n",
       "      <th>年龄</th>\n",
       "      <th>工资</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>157.50</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>15905.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>B</td>\n",
       "      <td>202.00</td>\n",
       "      <td>91.80</td>\n",
       "      <td>25.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>C</td>\n",
       "      <td>169.09</td>\n",
       "      <td>62.18</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>A</td>\n",
       "      <td>166.61</td>\n",
       "      <td>59.95</td>\n",
       "      <td>77.0</td>\n",
       "      <td>5434.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>B</td>\n",
       "      <td>185.19</td>\n",
       "      <td>NaN</td>\n",
       "      <td>62.0</td>\n",
       "      <td>4242.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   编号 地区      身高     体重    年龄       工资\n",
       "0   1  A  157.50    NaN  47.0  15905.0\n",
       "1   2  B  202.00  91.80  25.0      NaN\n",
       "2   3  C  169.09  62.18   NaN      NaN\n",
       "3   4  A  166.61  59.95  77.0   5434.0\n",
       "4   5  B  185.19    NaN  62.0   4242.0"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.read_csv('data/Missing_data_two.csv').head()"
   ]
  }
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