Revert "21"

This reverts commit 4ea4e3d4.

20.md

@@ -8,7 +8,7 @@
 
 ## MatPlotLib 中的双向条形图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -21,7 +21,7 @@ raw_data = {'first_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'post_score': [5, 43, 23, 23, 51]}
 df = pd.DataFrame(raw_data, columns = ['first_name', 'pre_score', 'mid_score', 'post_score'])
 df
-
+```
 
 |  | first_name | pre_score | mid_score | post_score |
 | --- | --- | --- | --- | --- |
@@ -31,7 +31,7 @@ df
 | 3 | Jake | 2 | 62 | 23 |
 | 4 | Amy | 3 | 70 | 51 |
 
-```py
+```
 # 输入数据，特别是第二和
 # 第三行，跳过第一列
 x1 = df.ix[1, 1:]
@@ -78,13 +78,13 @@ plt.xlim([-max(x2)-10, max(x1)+10])
 plt.grid()
 
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_back_to_back_bar_plot_6_0.png)
 
 ## MatPlotLib 中的条形图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -97,7 +97,7 @@ raw_data = {'first_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'post_score': [5, 43, 23, 23, 51]}
 df = pd.DataFrame(raw_data, columns = ['first_name', 'pre_score', 'mid_score', 'post_score'])
 df
-
+```
 
 |  | first_name | pre_score | mid_score | post_score |
 | --- | --- | --- | --- | --- |
@@ -107,7 +107,7 @@ df
 | 3 | Jake | 2 | 62 | 23 |
 | 4 | Amy | 3 | 70 | 51 |
 
-```py
+```
 # 为每个变量创建得分均值的列表
 mean_values = [df['pre_score'].mean(), df['mid_score'].mean(), df['post_score'].mean()]
 
@@ -146,13 +146,13 @@ plt.xticks(x_pos, bar_labels)
 plt.title('Mean Scores For Each Test')
 
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_bar_plot_6_0.png)
 
 ## Seaborn 中的调色板
 
-```py
+```
 import pandas as pd
 %matplotlib inline
 import matplotlib.pyplot as plt
@@ -173,164 +173,164 @@ df = pd.DataFrame(data, columns = ['date', 'battle_deaths', 'deaths_regiment_1',
 df = df.set_index(df.date)
 
 sns.palplot(sns.color_palette("deep", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_5_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("muted", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_6_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("bright", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_7_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("dark", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_8_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("colorblind", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_9_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("Paired", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_10_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("BuGn", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_11_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("GnBu", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_12_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("OrRd", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_13_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("PuBu", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_14_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("YlGn", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_15_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("YlGnBu", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_16_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("YlOrBr", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_17_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("YlOrRd", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_18_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("BrBG", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_19_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("PiYG", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_20_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("PRGn", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_21_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("PuOr", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_22_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("RdBu", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_23_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("RdGy", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_24_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("RdYlBu", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_25_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("RdYlGn", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_26_0.png)
 
-```py
+```
 sns.palplot(sns.color_palette("Spectral", 10))
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_27_0.png)
 
-```py
+```
 # 创建调色板并将其设为当前调色板
 flatui = ["#9b59b6", "#3498db", "#95a5a6", "#e74c3c", "#34495e", "#2ecc71"]
 sns.set_palette(flatui)
 sns.palplot(sns.color_palette())
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_29_0.png)
 
-```py
+```
 # 设置绘图颜色
 sns.tsplot([df.deaths_regiment_1, df.deaths_regiment_2, df.deaths_regiment_3, df.deaths_regiment_4,
             df.deaths_regiment_5, df.deaths_regiment_6, df.deaths_regiment_7], color="#34495e")
 
 # <matplotlib.axes._subplots.AxesSubplot at 0x116f5db70> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_color_palettes_31_1.png)
 
 ## 使用 Seaborn 和 pandas 创建时间序列绘图
 
-```py
+```
 import pandas as pd
 %matplotlib inline
 import matplotlib.pyplot as plt
@@ -353,23 +353,23 @@ sns.tsplot([df.deaths_regiment_1, df.deaths_regiment_2, df.deaths_regiment_3, df
             df.deaths_regiment_5, df.deaths_regiment_6, df.deaths_regiment_7], color="indianred")
 
 # <matplotlib.axes._subplots.AxesSubplot at 0x1140be780> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_pandas_timeseries_plot_5_1.png)
 
-```py
+```
 # 带有置信区间直线，但是没有直线的时间序列绘图
 sns.tsplot([df.deaths_regiment_1, df.deaths_regiment_2, df.deaths_regiment_3, df.deaths_regiment_4,
             df.deaths_regiment_5, df.deaths_regiment_6, df.deaths_regiment_7], err_style="ci_bars", interpolate=False)
 
 # <matplotlib.axes._subplots.AxesSubplot at 0x116400668> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_pandas_timeseries_plot_7_1.png)
 
 ## 使用 Seaborn 创建散点图
 
-```py
+```
 import pandas as pd
 %matplotlib inline
 import random
@@ -387,7 +387,7 @@ df['k'] = ['male','male','male','female','female']
 
 # 查看前几行数据
 df.head()
-
+```
 
 |  | x | y | z | k |
 | --- | --- | --- | --- | --- |
@@ -397,7 +397,7 @@ df.head()
 | 3 | 510 | 206 | 1 | female |
 | 4 | 848 | 357 | 0 | female |
 
-```py
+```
 # 设置散点图样式
 sns.set_context("notebook", font_scale=1.1)
 sns.set_style("ticks")
@@ -421,13 +421,13 @@ plt.xlabel('Time')
 plt.ylabel('Deaths')
 
 # <matplotlib.text.Text at 0x112b7bb70> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/seaborn_scatterplot_7_1.png)
 
 ## MatPlotLib 中的分组条形图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -439,7 +439,7 @@ raw_data = {'first_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'post_score': [5, 43, 23, 23, 51]}
 df = pd.DataFrame(raw_data, columns = ['first_name', 'pre_score', 'mid_score', 'post_score'])
 df
-
+```
 
 |  | first_name | pre_score | mid_score | post_score |
 | --- | --- | --- | --- | --- |
@@ -449,7 +449,7 @@ df
 | 3 | Jake | 2 | 62 | 23 |
 | 4 | Amy | 3 | 70 | 51 |
 
-```py
+```
 # 设置条形的位置和宽度
 pos = list(range(len(df['pre_score']))) 
 width = 0.25 
@@ -519,13 +519,13 @@ plt.ylim([0, max(df['pre_score'] + df['mid_score'] + df['post_score'])] )
 plt.legend(['Pre Score', 'Mid Score', 'Post Score'], loc='upper left')
 plt.grid()
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_grouped_bar_plot_6_0.png)
 
 ## MatPlotLib 中的直方图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -540,7 +540,7 @@ pd.set_option('display.max_columns', 50)
 
 df = pd.read_csv('https://www.dropbox.com/s/52cb7kcflr8qm2u/5kings_battles_v1.csv?dl=1')
 df.head()
-
+```
 
 |  | name | year | battle_number | attacker_king | defender_king | attacker_1 | attacker_2 | attacker_3 | attacker_4 | defender_1 | defender_2 | defender_3 | defender_4 | attacker_outcome | battle_type | major_death | major_capture | attacker_size | defender_size | attacker_commander | defender_commander | summer | location | region | note |
 | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
@@ -551,7 +551,7 @@ df.head()
 | 3 | Battle of the Green Fork | 298 | 4 | Robb Stark | Joffrey/Tommen Baratheon | Stark | NaN | NaN | NaN | Lannister | NaN | NaN | NaN | loss | pitched battle | 1 | 1 | 18000 | 20000 | Roose Bolton, Wylis Manderly, Medger Cerwyn, H... | Tywin Lannister, Gregor Clegane, Kevan Lannist... | 1 | Green Fork | The Riverlands | NaN |
 | 4 | Battle of the Whispering Wood | 298 | 5 | Robb Stark | Joffrey/Tommen Baratheon | Stark | Tully | NaN | NaN | Lannister | NaN | NaN | NaN | win | ambush | 1 | 1 | 1875 | 6000 | Robb Stark, Brynden Tully | Jaime Lannister | 1 | Whispering Wood | The Riverlands | NaN |
 
-```py
+```
 # 制作攻击方和防守方大小的两个变量
 # 但是当有超过 10000 个攻击方时将其排除在外
 data1 = df['attacker_size'][df['attacker_size'] < 90000]
@@ -584,11 +584,11 @@ plt.ylabel('Number of battles')
 plt.legend(loc='upper right')
 
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_histogram_6_0.png)
 
-```py
+```
 # 制作攻击方和防守方大小的两个变量
 # 但是当有超过 10000 个攻击方时将其排除在外
 data1 = df['attacker_size'][df['attacker_size'] < 90000]
@@ -634,13 +634,13 @@ plt.ylabel('Number of battles')
 plt.legend(loc='upper right')
 
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_histogram_8_0.png)
 
 ## 从 Pandas 数据帧生成 MatPlotLib 散点图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -654,7 +654,7 @@ raw_data = {'first_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'postTestScore': [25, 94, 57, 62, 70]}
 df = pd.DataFrame(raw_data, columns = ['first_name', 'last_name', 'age', 'female', 'preTestScore', 'postTestScore'])
 df
-
+```
 
 |  | first_name | last_name | age | female | preTestScore | postTestScore |
 | --- | --- | --- | --- | --- | --- | --- |
@@ -664,30 +664,30 @@ df
 | 3 | Jake | Milner | 24 | 0 | 2 | 62 |
 | 4 | Amy | Cooze | 73 | 1 | 3 | 70 |
 
-```py
+```
 # preTestScore 和 postTestScore 的散点图
 # 每个点的大小取决于年龄
 plt.scatter(df.preTestScore, df.postTestScore
 , s=df.age)
 
 # <matplotlib.collections.PathCollection at 0x10ca42b00> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_scatterplot_from_pandas_6_1.png)
 
-```py
+```
 # preTestScore 和 postTestScore 的散点图
 # 大小为 300，颜色取决于性别
 plt.scatter(df.preTestScore, df.postTestScore, s=300, c=df.female)
 
 # <matplotlib.collections.PathCollection at 0x10cb90a90> 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_scatterplot_from_pandas_8_1.png)
 
 ## Matplotlib 的简单示例
 
-```py
+```
 # 让 Jupyter 加载 matplotlib 
 # 并内联创建所有绘图（也就是在页面上）
 %matplotlib inline
@@ -697,13 +697,13 @@ import matplotlib.pyplot as pyplot
 pyplot.plot([1.6, 2.7])
 
 # [<matplotlib.lines.Line2D at 0x10c4e7978>] 
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_simple_example_6_1.png)
 
 ## MatPlotLib 中的饼图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -714,7 +714,7 @@ raw_data = {'officer_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'march_arrests': [5, 43, 23, 23, 51]}
 df = pd.DataFrame(raw_data, columns = ['officer_name', 'jan_arrests', 'feb_arrests', 'march_arrests'])
 df
-
+```
 
 |  | officer_name | jan_arrests | feb_arrests | march_arrests |
 | --- | --- | --- | --- | --- |
@@ -724,11 +724,11 @@ df
 | 3 | Jake | 2 | 62 | 23 |
 | 4 | Amy | 3 | 70 | 51 |
 
-```py
+```
 # 创建一列，其中包含每个官员的总逮捕数
 df['total_arrests'] = df['jan_arrests'] + df['feb_arrests'] + df['march_arrests']
 df
-
+```
 
 |  | officer_name | jan_arrests | feb_arrests | march_arrests | total_arrests |
 | --- | --- | --- | --- | --- | --- |
@@ -738,7 +738,7 @@ df
 | 3 | Jake | 2 | 62 | 23 | 87 |
 | 4 | Amy | 3 | 70 | 51 | 124 |
 
-```py
+```
 # （从 iWantHue）创建一列颜色
 colors = ["#E13F29", "#D69A80", "#D63B59", "#AE5552", "#CB5C3B", "#EB8076", "#96624E"]
 
@@ -766,13 +766,13 @@ plt.axis('equal')
 # 查看绘图
 plt.tight_layout()
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_pie_chart_7_0.png)
 
 ## MatPlotLib 中的散点图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -786,7 +786,7 @@ pd.set_option('display.max_columns', 50)
 
 df = pd.read_csv('https://raw.githubusercontent.com/chrisalbon/war_of_the_five_kings_dataset/master/5kings_battles_v1.csv')
 df.head()
-
+```
 
 |  | name | year | battle_number | attacker_king | defender_king | attacker_1 | attacker_2 | attacker_3 | attacker_4 | defender_1 | defender_2 | defender_3 | defender_4 | attacker_outcome | battle_type | major_death | major_capture | attacker_size | defender_size | attacker_commander | defender_commander | summer | location | region | note |
 | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
@@ -796,7 +796,7 @@ df.head()
 | 3 | Battle of the Green Fork | 298 | 4 | Robb Stark | Joffrey/Tommen Baratheon | Stark | NaN | NaN | NaN | Lannister | NaN | NaN | NaN | loss | pitched battle | 1.0 | 1.0 | 18000.0 | 20000.0 | Roose Bolton, Wylis Manderly, Medger Cerwyn, H... | Tywin Lannister, Gregor Clegane, Kevan Lannist... | 1.0 | Green Fork | The Riverlands | NaN |
 | 4 | Battle of the Whispering Wood | 298 | 5 | Robb Stark | Joffrey/Tommen Baratheon | Stark | Tully | NaN | NaN | Lannister | NaN | NaN | NaN | win | ambush | 1.0 | 1.0 | 1875.0 | 6000.0 | Robb Stark, Brynden Tully | Jaime Lannister | 1.0 | Whispering Wood | The Riverlands | NaN |
 
-```py
+```
 # 创建图形
 plt.figure(figsize=(10,8))
 
@@ -863,13 +863,13 @@ plt.xlim([min(df['attacker_size'])-1000, max(df['attacker_size'])+1000])
 plt.ylim([min(df['defender_size'])-1000, max(df['defender_size'])+1000])
 
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_simple_scatterplot_6_0.png)
 
 ## MatPlotLib 中的栈式百分比条形图
 
-```py
+```
 %matplotlib inline
 import pandas as pd
 import matplotlib.pyplot as plt
@@ -880,7 +880,7 @@ raw_data = {'first_name': ['Jason', 'Molly', 'Tina', 'Jake', 'Amy'],
         'post_score': [5, 43, 23, 23, 51]}
 df = pd.DataFrame(raw_data, columns = ['first_name', 'pre_score', 'mid_score', 'post_score'])
 df
-
+```
 
 |  | first_name | pre_score | mid_score | post_score |
 | --- | --- | --- | --- | --- |
@@ -890,7 +890,7 @@ df
 | 3 | Jake | 2 | 62 | 23 |
 | 4 | Amy | 3 | 70 | 51 |
 
-```py
+```
 # 创建带有一个子图的图形
 f, ax = plt.subplots(1, figsize=(10,5))
 
@@ -981,6 +981,6 @@ plt.setp(plt.gca().get_xticklabels(), rotation=45, horizontalalignment='right')
 
 # 展示绘图
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/python/data_visualization/matplotlib_percentage_stacked_bar_plot_6_0.png)

21.md

@@ -20,7 +20,7 @@ $ s^2 = \frac {1}{n-1} \sum_{i=1}^n \left(x_i - \overline{x} \right)^ 2 $
 
 ## 演示中心极限定律
 
-```py
+```
 # 导入包
 import pandas as pd
 import numpy as np
@@ -39,11 +39,11 @@ population['numbers'] = np.random.uniform(0,10000,size=10000)
 population['numbers'].hist(bins=100)
 
 # <matplotlib.axes._subplots.AxesSubplot at 0x112c72710> 
-
+```
 
 ![png](https://chrisalbon.com/statistics/frequentist/demonstrate_the_central_limit_theorem_5_1.png)
 
-```py
+```
 # 查看数值的均值
 population['numbers'].mean()
 
@@ -63,13 +63,13 @@ for i in range(0,1000):
 pd.Series(sampled_means).hist(bins=100)
 
 # <matplotlib.axes._subplots.AxesSubplot at 0x11516e668> 
-
+```
 
 ![png](https://chrisalbon.com/statistics/frequentist/demonstrate_the_central_limit_theorem_11_1.png)
 
 这是关键的图表，记住总体分布是均匀的，然而，这个分布接近正态。 这是中心极限理论的关键点，也是我们可以假设样本均值是无偏的原因。
 
-```py
+```
 # 查看 sampled_means 的均值
 pd.Series(sampled_means).mean()
 
@@ -82,25 +82,25 @@ error = population['numbers'].mean() - pd.Series(sampled_means).mean()
 print('The Mean Sample Mean is only %f different the True Population mean!' % error)
 
 # The Mean Sample Mean is only 2.359302 different the True Population mean! 
-
+```
 
 ## 皮尔逊相关系数
 
 基于 [cbare](http://stackoverflow.com/users/199166/cbare) 的[这个](http://stackoverflow.com/a/17389980/2935984) StackOverflow 答案。
 
-```py
+```
 import statistics as stats
 
 x = [1,2,3,4,5,6,7,8,9]
 y = [2,1,2,4.5,7,6.5,6,9,9.5]
-
+```
 有许多等价的表达方式来计算皮尔逊相关系数（也称为皮尔逊的 r）。这是一个。
 
 $r={\frac {1}{n-1}}\sum_{i=1}^{n}\left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)\left({\frac {y_{i}-{\bar {y}}}{s_{y}}}\right)$
 
 其中 $s_{x}$ 和 $s_{y}$ 是 $x$ 和 $y $ 的标准差，$\left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)$ 是 $x$ 和 $y$ 的[标准得分](https://en.wikipedia.org/wiki/Standard_score)。
 
-```py
+```
 # 创建函数
 def pearson(x,y):
 
@@ -142,11 +142,11 @@ def pearson(x,y):
 pearson(x,y)
 
 # 0.9412443251336238 
-
+```
 
 ## 概率质量函数（PMF）
 
-```py
+```
 # 加载库
 import matplotlib.pyplot as plt
 
@@ -175,13 +175,13 @@ for unique_value, count in count.items():
 # 绘制概率质量函数
 plt.bar(list(probability_mass_function.keys()), probability_mass_function.values(), color='g')
 plt.show()
-
+```
 
 ![png](https://chrisalbon.com/statistics/frequentist/probability_mass_functions_10_0.png)
 
 ## Spearman 排名相关度
 
-```py
+```
 import numpy as np
 import pandas as pd
 import scipy.stats
@@ -189,11 +189,11 @@ import scipy.stats
 # 创建两列随机变量
 x = [1,2,3,4,5,6,7,8,9]
 y = [2,1,2,4.5,7,6.5,6,9,9.5]
-
+```
 
 Spearman 的排名相关度，是变量的排名版本的皮尔逊相关系数。
 
-```py
+```
 # 创建接受 x 和 y 的函数
 def spearmans_rank_correlation(xs, ys):
 
@@ -216,11 +216,11 @@ spearmans_rank_correlation(x, y)[0]
 scipy.stats.spearmanr(x, y)[0]
 
 # 0.90377360145618102 
-
+```
 
 ## T 检验
 
-```py
+```
 from scipy import stats
 import numpy as np
 
@@ -231,13 +231,13 @@ x = np.random.normal(1, 1.5, 20)
 # 创建 20 个观测的列表，从均值为 0，
 # 标准差为 1.5 的正态分布中随机抽取
 y = np.random.normal(0, 1.5, 20)
-
+```
 
 ### 单样本双边 T 检验
 
 想象一下单样本 T 检验，并绘制一个“正态形状的”山丘，以`1`为中心，并以`1.5`为标准差而“展开”，然后在`0`处放置一个标志并查看标志在山丘上的位置。它靠近顶部吗？ 或者远离山丘？ 如果标志靠近山丘的底部或更远，则 t 检验的 p 值将低于`0.05`。
 
-```py
+```
 # 运行 T 检验来检验 x 的均值和 0 相比，是否有统计学显著的差异
 pvalue = stats.ttest_1samp(x, 0)[1]
 
@@ -245,13 +245,13 @@ pvalue = stats.ttest_1samp(x, 0)[1]
 pvalue
 
 # 0.00010976647757800537 
-
+```
 
 ### 双样本非配对等方差双边 T 检验
 
 想象一下单样本 T 检验，并根据标准差绘制两个（正态形状的）山丘，以它们的均值为中心，并根据他们的标准差绘制它们的“平坦度”（个体延展度）。 T 检验考察了两座山丘重叠的程度。 它们基本上是彼此覆盖的吗？ 山丘的底部几乎没有碰到吗？ 如果山丘的尾部刚刚重叠或根本不重叠，则 t 检验的 p 值将低于 0.05。
 
-```py
+```
 stats.ttest_ind(x, y)[1]
 
 # 0.00035082056802728071 
@@ -259,27 +259,27 @@ stats.ttest_ind(x, y)[1]
 stats.ttest_ind(x, y, equal_var=False)[1]
 
 # 0.00035089238660076095 
-
+```
 
 ### 双样本配对双边 T 检验
 
 当我们采集重复样本，并且想要考虑我们正在测试的两个分布是成对的这一事实时，使用配对 T 检验。
 
-```py
+```
 stats.ttest_rel(x, y)[1]
 
 # 0.00034222792790150386 
-
+```
 
 ## 方差和标准差
 
-```py
+```
 # 导入包
 import math
 
 # 创建值的列表
 data = [3,2,3,4,2,3,5,2,2,33,3,5,2,2,5,6,62,2,2,3,6,6,2,23,3,2,3]
-
+```
 
 方差是衡量数据分布延展度的指标。 方差越大，数据点越“分散”。 方差，通常表示为 $ S^{2}$，计算方式如下：
 
@@ -289,7 +289,7 @@ $ \text{Sample Variance} = S_{n-1}^{2} = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x}
 
 其中 $n$ 是观测数，$\bar{x}$ 是观察值的平均值，$x_i-\bar{x}$ 是单个观察值减去数据均值。 请注意，如果我们根据来自该总体的样本估计总体的方差，我们应该使用第二个等式，将 $n$ 替换为 $n-1$。
 
-```py
+```
 # 计算 n
 n = len(data)
 
@@ -321,11 +321,11 @@ population_variance = sum_of_deviations_from_mean_squared/n
 population_variance 
 
 # 160.78463648834017 
-
+```
 
 标准差就是方差的平方根。
 
-```py
+```
 # 计算总体方差的平方根
 population_standard_deviation = math.sqrt(population_variance)
 
@@ -333,3 +333,4 @@ population_standard_deviation = math.sqrt(population_variance)
 population_standard_deviation
 
 # 12.68008818929664 
+```
\ No newline at end of file