九、总体和样本

import pandas as pd
import numpy as np
# Create a Population DataFrame with 10 data 

data = pd.DataFrame()
data['Population'] = [47, 48, 85, 20, 19, 13, 72, 16, 50, 60]

You may get different results from sampling.

# Draw sample with replacement, size=5 from Population

a_sample_with_replacement = data['Population'].sample(5, replace=True)
print(a_sample_with_replacement)

4 19
8 50
5 13
1 48
2 85
Name: Population, dtype: int64

# Draw sample without replacement, size=5 from Population

a_sample_without_replacement = data['Population'].sample(5, replace=False)
print(a_sample_without_replacement)

8 50
2 85
4 19
6 72
1 48
Name: Population, dtype: int64

Parameters and Statistics

# Calculate mean and variance
population_mean = None
population_var = None
print('Population mean is ', population_mean)
print('Population variance is', population_var)

Expected Output: Population mean is 43.0 Population variance is 571.8

You may get different result from sampling.

# Calculate sample mean and sample standard deviation, size =10
# You will get different mean and varince every time when you excecute the below code

a_sample = data['Population'].sample(10, replace=True)
sample_mean = a_sample.mean()
sample_var = a_sample.var()
print('Sample mean is ', sample_mean)
print('Sample variance is', sample_var)

Sample mean is 48.4
Sample variance is 712.488888889

Average of an unbiased estimator

sample_length = 500
sample_variance_collection=[data['Population'].sample(10, replace=True).var(ddof=1) for i in range(sample_length)]