10. 数值统计运算.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 统计运算\n",
    "这一章包含数据分析用得最多的函数操作。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    @auther: sunzhenhang\n",
    "    @zhihu: https://www.zhihu.com/people/HANGZS/activities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E:\\ML\\实战\\pandas实用教程 - 副本\n"
     ]
    }
   ],
   "source": [
    "!cd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 1. 数值型统计运算\n",
    "这些统计操作只对元素类型为数值型的列有效，返回以列索引或行索引为索引的Series。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 一元统计\n",
    "顾名思义，这些统计只是自身分布情况的反映。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.1 `.sum()`\n",
    "#### `DataFrame.sum(axis='index')`\n",
    "- axis：'index'-沿列加，'columns'-沿行加"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
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       "      <th>B</th>\n",
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       "   A  B\n",
       "a  1  2\n",
       "b  3  5"
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     "execution_count": 12,
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   ],
   "source": [
    "df = pd.DataFrame([[1,2],[3,5]], index = ['a','b'],columns = ['A','B'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    4\n",
       "B    7\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sum()  # 按列加"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    3\n",
       "b    8\n",
       "dtype: int64"
      ]
     },
     "execution_count": 14,
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   "source": [
    "df.sum(axis = 'columns')  # 按行加"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.2 `.mean(), .std(), .var()`\n",
    "均值、标准差、方差"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.3 `.max(), .min(), .median()`\n",
    "最大、最小、中值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    0.75\n",
       "B    0.75\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.mad(axis = 'index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 二元统计\n",
    "计算任意两列直接的统计量，返回以列索引为新行索引和列索引的DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2.1 `.cov()`\n",
    "#### `DataFrame.cov(min_periods=None)`\n",
    "- min_periods：每一列去除NaN后，要求能够参与运算的最少元素个数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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       "   B  C\n",
       "0  1  2\n",
       "1  2  0"
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     "execution_count": 41,
     "metadata": {},
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   ],
   "source": [
    "df1 = pd.DataFrame([[1,2],[2,0]],columns = ['B','C'])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
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       "     B    C\n",
       "B  0.5 -1.0\n",
       "C -1.0  2.0"
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     "execution_count": 42,
     "metadata": {},
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   ],
   "source": [
    "df1.cov()"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2.2 `.corr()`\n",
    "相关系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
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       "     B    C\n",
       "B  1.0 -1.0\n",
       "C -1.0  1.0"
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     "execution_count": 43,
     "metadata": {},
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   "source": [
    "df1.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2.3 `.corrwith()`\n",
    "corr是自身列之间的关系，而这个函数可以对不同的DataFrame进行运算，不要要记得运算发生在**同名列和同索引的行**之间。\n",
    "#### `DataFrame.corrwith(other, axis=0, drop=False)`\n",
    "- other：另一个DataFrame或Series\n",
    "- axis：'index'或'columns'\n",
    "- drop：是否丢掉结果中的NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
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       "   B  C\n",
       "0  1  2\n",
       "1  2  0\n",
       "2  2  3"
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     "execution_count": 62,
     "metadata": {},
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   ],
   "source": [
    "df1 = pd.DataFrame([[1,2],[2,0],[2,3]],index = [0,1,2],columns = ['B','C'])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
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       "   A  B\n",
       "0  1  2\n",
       "1  2  0"
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   "source": [
    "df"
   ]
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  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    NaN\n",
       "B   -1.0\n",
       "C    NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corrwith(df1)  #只对 同名列 和 同名行 进行计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    2\n",
       "Name: B, dtype: int64"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([1,2], index = [0,1], name = 'B')\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": true
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       "   A  B\n",
       "0  1  2\n",
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    "df"
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  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    1.0\n",
       "B   -1.0\n",
       "dtype: float64"
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     "execution_count": 72,
     "metadata": {},
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    "df.corrwith(s)"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "# 2. 类型型统计运算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1. `value_counts()`\n",
    "不适合DataFrame。\n",
    "#### `Series/Index.value_counts(normalize=False, ascending=False, bins=None)`\n",
    "- normalize：True or False，计算频次或者频率比；\n",
    "- ascending：True or False，排序方式，默认降序；\n",
    "- bins：int，pd.cut的一种快捷操作，对连续数值型效果好；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    2\n",
       "2    1\n",
       "3    2\n",
       "4    1\n",
       "5    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series([1,2,1,2,1,3])\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    3\n",
       "2    2\n",
       "3    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3    1\n",
       "2    2\n",
       "1    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.value_counts(ascending = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.997, 2.0]    5\n",
       "(2.0, 3.0]      1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.value_counts( bins = 2)   # bins按照int平均分割，左开右闭，左侧外延1%以包含最左值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 `.count()`\n",
    "计算统计每一类non-NaN元素个数，这个函数可以快速了解哪些特征或哪些样本缺失比较严重。\n",
    "#### `DataFrame.count(axis=0)`\n",
    "- axis: 0-查看列，1-查看行；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
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       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A  B\n",
       "0  1  2\n",
       "1  2  0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    2\n",
       "B    2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.count(axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2\n",
       "1    2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.count(axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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