Python statistics pvariance()用法及代碼示例

先決條件：Python統計信息| variance()

pvariance() 函數有助於計算整個方差，而不是樣本方差。之間的唯一區別variance()和pvariance()是在使用variance()時，僅考慮樣本均值，而在pvariance()期間，則考慮整個總體的均值。

總體方差與樣本方差相似，它說明了特定總體中的數據點如何分布。它是從data-points到data-set均值的平均距離，為平方。總體方差是總體的一個參數，不依賴於研究方法或抽樣方法。

用法： pvariance( [data], mu)

Parameters:
[數據]：具有實值數字的可迭代項。
mu (optional):將data-set /人口的實際平均值作為值。

Returnype:返回作為參數傳遞的值的實際總體方差。

Exceptions:
StatisticsError為data-set引發的值小於作為參數傳遞的2個值。
不可能的價值當以mu形式提供的值與data-set的實際平均值不匹配時。

代碼1：

# Pythom code to demonstrate the 
# use of pvariance() 
  
# importing statistics module 
import statistics 
  
# creating a random population list 
population = (1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.9, 2.2, 
              2.3, 2.4, 2.6, 2.9, 3.0, 3.4, 3.3, 3.2) 
  
  
# Prints the population variance 
print("Population variance is %s" 
      %(statistics.pvariance(population)))

輸出：

Population variance is 0.6658984375

代碼2：在不同範圍的種群樹上演示pvariance()。

# Python code to demonstrate pvariance() 
# on various range of population sets 
  
# importing statistics module 
from statistics import pvariance 
  
# importing fractions module as F 
from fractions import Fraction as F 
  
  
# Population tree for a set of positive integers 
pop1 = (1, 2, 3, 5, 4, 6, 1, 2, 2, 3, 1, 3, 
         7, 8, 9, 1, 1, 1, 2, 6, 7, 8, 9, ) 
  
# Creating a population tree for 
# a set of negative integers 
pop2 = (-36, -35, -34, -32, -30, -31, -33, -33, -33, 
             -38, -36, -35, -34, -38, -40, -31, -32) 
  
# Creating a population tree for 
# a set of fractional numbers 
pop3 = (F(1, 3), F(2, 4), F(2, 3), 
        F(3, 2), F(2, 5), F(2, 2), 
        F(1, 1), F(1, 4), F(1, 2), F(2, 1)) 
  
# Creating a population tree for 
# a set of decimal values 
pop4 = (3.45, 3.2, 2.5, 4.6, 5.66, 6.43, 
        4.32, 4.23, 6.65, 7.87, 9.87, 1.23, 
            1.00, 1.45, 10.12, 12.22, 19.88) 
  
# Print the population variance for 
# the created population trees 
print("Population variance of set 1 is % s"
                        %(pvariance(pop1))) 
                          
print("Population variance of set 2 is % s" 
                        %(pvariance(pop2))) 
                          
print("Population variance of set 3 is % s" 
                        %(pvariance(pop3))) 
                          
print("Population variance of set 4 is % s" 
                        %(pvariance(pop4)))

輸出：

Population variance of set 1 is 7.913043478260869
Population variance of set 2 is 7.204152249134948
Population variance of set 3 is 103889/360000
Population variance of set 4 is 21.767923875432526

代碼3：演示使用mu參數。

# Python code to demonstrate the use 
#  of 'mu' parameter on pvariance() 
  
# importing statistics module 
import statistics 
  
# Apparently, the Python interpreter doesn't 
# even check whether the value entered for mu 
# is the actual mean of data-set or not. 
# Thus providing incorrect value would 
# lead to impossible answers 
  
# Creating a population tree of the 
# age of kids in a locality 
tree = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 
        12, 12, 12, 12, 13, 1, 2, 12, 2, 2, 
              2, 3, 4, 5, 5, 5, 5, 6, 6, 6) 
  
# Finding the mean of population tree 
m = statistics.mean(tree) 
  
# Using the mu parameter 
# while using pvariance() 
print("Population Variance is % s" 
      %(statistics.pvariance(tree, mu = m)))

輸出：

Population Variance is 14.30385015608741

代碼4：演示pvariance()和variance()之間的區別

# Pythom code to demonstrate the  
# difference between pvariance()  
# and variance() 
  
# importing statistocs module 
import statistics 
  
# Population tree and extract 
# a sample from it 
tree = (1.1, 1.22, .23, .55, .67, 2.33, 2.81, 
             1.54, 1.2, 0.2, 0.1, 1.22, 1.61) 
  
# Sample extract from population tree 
sample = (1.22, .23, .55, .67, 2.33, 
               2.81, 1.54, 1.2, 0.2) 
  
  
# Print sample variance and as  
# well as population variance 
print ("Variance of whole popuation is %s" 
            %(statistics.pvariance(tree))) 
              
print ("Variance of sample from population is %s "
                 % (statistics.variance(sample))) 
  
# Print the difference in both population  
# variance and sample variance 
print("\n") 
  
print("Difference in Population variance"
            "and Sample variance is % s" 
        %(abs(statistics.pvariance(tree)  
        - statistics.variance(sample))))

輸出：

Variance of the whole popuation is 0.6127751479289941
Variance of the sample from population is 0.8286277777777779 

Difference in Population variance and Sample variance is 0.21585262984878373

注意：從上麵的示例示例中可以看出，總體方差和示例方差相差不大。

代碼5：展示StatisticsError

# Python code to demonstrate StatisticsError 
  
# importing statistics module 
import statistics 
  
# creating an empty population set 
pop = () 
  
# will raise StatisticsError 
print(statistics.pvariance(pop))

輸出：

Traceback (most recent call last):
  File "/home/fa112e1405f09970eeddd48214318a3c.py", line 10, in 
    print(statistics.pvariance(pop))
  File "/usr/lib/python3.5/statistics.py", line 603, in pvariance
    raise StatisticsError('pvariance requires at least one data point')
statistics.StatisticsError:pvariance requires at least one data point

應用範圍：
總體方差的應用與樣本方差非常相似，盡管總體方差的範圍比樣本方差大得多。僅在要計算整個總體的方差時才使用總體方差，否則在計算樣本方差時，最好使用variance()。人口差異是統計和處理大量數據中非常重要的工具。就像，當無所不知的均值是未知的(樣本均值)時，方差被用作偏差估計量。

相關用法

注：本文由純淨天空篩選整理自retr0大神的英文原創作品 Python statistics | pvariance()。非經特殊聲明，原始代碼版權歸原作者所有，本譯文未經允許或授權，請勿轉載或複製。