Pandas 中的系统采样

抽样是一种方法，可以从给定的数据中提取子集（样本），并对样本进行调查，而无需调查数据的每一件事。例如，假设在一所大学里，有人想检查在这所大学学习的学生的平均身高。一种方法是收集所有学生的数据并进行计算，但这项任务非常耗时。因此，使用采样。因此，解决方案是在课间休息期间，从食堂中随机选择学生并测量他们的身高，然后根据该学生的子集计算平均身高。

采样类型：

采样

系统抽样

系统抽样被定义为概率抽样的类型，研究人员可以在其中研究来自大量数据的目标数据。通过选择随机起点来选择目标数据，并在一定间隔后从中选择下一个元素作为样本。在这种情况下，从大数据中提取了一个小子集（样本）。

假设数据的大小为D ， N将是我们要选择的样本大小。所以根据系统抽样：

Interval = (D/N)

Suppose (D/N) = J

So when we choose first random element E from Data , the next element for Sample would be (E+J)

Example : Total Size of Data  = 50 (1 to 50)

          We want elements in  Sample = 5

          Interval = 50/5 = 10 .

It means in a sample we want gapping of 10 elements Systematically.

Suppose i randomly choose element first Sample Element  = 5

So next would be 5+10 = 15

                 15+10= 25

                 25+ 10 =35

                 35+10  = 45

So, 

Sample = { 5,15,25,35,45 }

从图上看，

方法：

• 取数据。
• 从大数据中提取系统样本。
• 打印样本数据的平均值。

程序：

Python3

# Import in order to use inbuilt functions
import numpy as np
import pandas as pd
 
# Define total number of students
number_of_students = 15
 
# Create data dictionary
data = {'Id': np.arange(1, number_of_students+1).tolist(),
        'height': [159, 171, 158, 162, 162, 177, 160, 175,
                   168, 171, 178, 178, 173, 177, 164]}
 
# Transform dictionary into a data frame
df = pd.DataFrame(data)
 
display(df)
 
# Define systematic sampling function
def systematic_sampling(df, step):
 
    indexes = np.arange(0, len(df), step=step)
    systematic_sample = df.iloc[indexes]
    return systematic_sample
 
 
# Obtain a systematic sample and save it in a new variable
systematic_sample = systematic_sampling(df, 3)
 
# View sampled data frame
display(systematic_sample)

输出：

示例：打印样本数据的平均值

蟒蛇3

# Import in order to use inbuilt functions
import numpy as np
import pandas as pd
 
# Define total number of students
number_of_students = 15
 
# Create data dictionary
data = {'Id': np.arange(1, number_of_students+1).tolist(),
        'height': [159, 171, 158, 162, 162, 177, 160, 175,
                   168, 171, 178, 178, 173, 177, 164]}
 
# Transform dictionary into a data frame
df = pd.DataFrame(data)
 
 
# Define systematic sampling function
def systematic_sampling(df, step):
 
    indexes = np.arange(0, len(df), step=step)
    systematic_sample = df.iloc[indexes]
    return systematic_sample
 
 
# Obtain a systematic sample and save it in a new variable
systematic_sample = systematic_sampling(df, 3)
 
# View sampled data frame
display(systematic_sample)
 
# Empty Print Statement for new line
print()
 
# Save the sample data in a separate variable
systematic_data = round(systematic_sample['height'].mean())
print("Average Height in cm: ", systematic_data)

输出：

系统抽样的类型

系统抽样分为以下三种类型：

系统抽样的类型

系统随机抽样：

在系统随机抽样中，选择随机起点，然后从该随机起点应用系统抽样。

方法：

• 获取数据
• 选择一个随机起点
• 对数据应用系统方法
• 按预期执行操作

例子：

蟒蛇3

# Import in order to use inbuilt functions
import numpy as np
import pandas as pd
import random
 
# Define total number of house
number_of_house = 30
 
# Create data dictionary
data = {'house_number': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
                         14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
                         24, 25, 26, 27, 28, 29, 30],
        'number_of_children': [2, 2, 1, 3, 2, 1, 4, 1, 3, 5, 4, 3, 5,
                               3, 2, 1, 2, 3, 4, 5, 3, 4, 5, 2, 2, 2,
                               2, 3, 2, 1]}
 
# Transform dictionary into a data frame
df = pd.DataFrame(data)
 
# Defining Size of Systematic Sample
size_of_systematic_sample = 6
 
# Defining Interval(gap) in order to get required data.
interval = (number_of_house // size_of_systematic_sample)
 
# Choosing Random Number
random_number = random.randint(1, 30)
 
# Define systematic sampling function
def systematic_sampling(df, step):
 
    indexes = np.arange(random_number, len(df), step=step)
    systematic_sample = df.iloc[indexes]
    return systematic_sample
 
 
# Obtain a systematic sample and save it in a new variable
systematic_sample = systematic_sampling(df, interval)
 
# View sampled data frame
display(systematic_sample)
 
# Empty Print Statement for new line
print()
 
# Save the sample data in a separate variable
systematic_data = round(systematic_sample['number_of_children'].mean())
 
# Printing Average Number of Children
print("Average Number Of Childrens in Locality: ", systematic_data)

输出：

线性系统采样：

线性系统抽样是一种系统抽样，其中使用线性方法选择样本。线性方法，在特定时间间隔后从大数据中选择样本，然后对选定的样本执行操作。

元素在范围starting_random_number 到last_element -1 之间选择。

方法：

• 获取数据
• 在特定时间间隔后从数据集中选择数据
• 按预期执行操作

例子：

蟒蛇3

# Import in order to use inbuilt functions
import numpy as np
import pandas as pd
import random
 
# Define total number of boxes
number_of_boxes = 30
 
# Create data dictionary
data = {'Box_Number': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
                       15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
                       27, 28, 29, 30],
         
        'Defective_Bulbs': [2, 2, 1, 0, 2, 1, 0, 1, 3, 5, 4, 3, 5, 3,
                            0, 1, 2, 0, 4, 5, 3, 4, 5, 2, 0, 3, 2, 0,
                            5, 4]}
 
# Transform dictionary into a data frame
df = pd.DataFrame(data)
 
 
# Size of Systematic Sample
size_systematic_sample = 5
 
# Interval (Gap) taken
interval = (number_of_boxes // size_systematic_sample)
 
# Choosing Random Starting Point
random_number = random.randint(1, 30)
 
# Define systematic sampling function
def systematic_sampling(df, step):
 
    indexes = np.arange(random_number, len(df)-1, step=step)
    systematic_sample = df.iloc[indexes]
    return systematic_sample
 
 
# Obtain a systematic sample and save it in a new variable
systematic_sample = systematic_sampling(df, interval)
 
# View sampled data frame
display(systematic_sample)
 
# Empty Print Statement for new line
print()
 
# Save the sample data in a separate variable
systematic_data = round(systematic_sample['Defective_Bulbs'].mean())
 
# Printing Average Number of Defective Bulbs
print("Average Number Of Defective Bulbs: ", systematic_data)

输出：

循环系统抽样

在循环系统抽样中，样本结束后再次从同一点开始。基本上，在系统地选择样本时，当到达结束元素时，样本的选择将再次从头开始，直到样本的所有元素都被选中。这意味着对使用循环系统采样选择的所有数据执行操作。

方法：

• 获取数据
• 系统地选择样品
• 到达结束后，重新启动
• 按预期执行操作

程序：

蟒蛇3

# Import in order to use inbuilt functions
import numpy as np
import pandas as pd
import random
 
# Define total number of house
number_of_house = 30
 
# Create data dictionary
data = {'house_number': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
                         14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
                         24, 25, 26, 27, 28, 29, 30],
        'number_of_Adults': [2, 2, 5, 3, 2, 8, 4, 7, 8, 5, 4, 9, 5,
                             4, 2, 3, 2, 3, 4, 5, 6, 4, 5, 4, 2, 6,
                             2, 3, 2, 2]}
 
# Transform dictionary into a data frame
df = pd.DataFrame(data)
 
# Defining Size of Systematic Sample
size_of_systematic_sample = 6
 
 
# Defining Interval(gap) in order to get required data.
interval = (number_of_house // size_of_systematic_sample)
 
# Define systematic sampling function
def systematic_sampling(df, step):
    indexes = np.arange(0, len(df), step=step)
    systematic_sample = df.iloc[indexes]
    return systematic_sample
 
 
# Obtain a systematic sample and save it in a new variable
systematic_sample = systematic_sampling(df, interval)
 
# View sampled data frame
display(systematic_sample)
 
 
# Empty Print Statement for new line
print()
 
# Save the sample data in a separate variable
systematic_data = round(systematic_sample['number_of_Adults'].mean())
 
# Printing Average Number of Children
print("Average Number Of Adults in Locality: ", systematic_data)

输出：