Python中的harmonic_mean()

Harmonic Mean（也称为Contrary Mean）是几种平均值中的一种，特别是毕达哥拉斯平均值之一。通常用于需要平均费率的情况。调和平均值也是给定一组观察值的倒数的算术平均值的倒数。

例如，1、4 和 4 的调和平均值可以计算为：

${\displaystyle \left({\frac {1^{-1}+4^{-1}+4^{-1}}{3}}\right)^{-1}={\frac {3}{{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{4}}}}={\frac {3}{1.5}}=2\, }$

通过使用统计模块中的harmonic_mean()函数，可以将谐波平均值合并到Python3 中。

Syntax : harmonic_mean([data-set])
Parameters : 
[data-set]: which is a list or tuple or iterator of real valued numbers.
Returntype : Returns the harmonic_mean of the given set of data.
Errors and Exceptions :
StatisticsError when a empty data-set is passed or if data-set consist of negative values. 
TypeError for dataset of non-numeric type values. 
 

注意：谐波平均值仅使用列表、集合或任何序列中的正值计算。代码#1：

Python3

# Python3 code to demonstrate the
# working of harmonic_mean() function
 
# Import statistics module
import statistics
 
# list of positive real valued numbers
data = [1, 3, 5, 7, 9]
 
# using harmonic mean function to calculate
# the harmonic mean of the given data-set
print("Harmonic Mean is % s " % (statistics.harmonic_mean(data)))

输出 ：

Harmonic Mean is 2.797513321492007 

代码#2：

Python3

# Python3 program to demonstrate harmonic_mean()
# function from the statistics module
 
# Importing the statistics module
from statistics import harmonic_mean
 
# Importing fractions module as fr
from fractions import Fraction as fr
 
# tuple of positive integer numbers
data1 = (2, 3, 4, 5, 7, 9, 11)
 
# tuple of a set of floating-point values
data2 = (2.4, 5.1, 6.7, 8.9)
 
# tuple of a set of fractional numbers
data3 = (fr(1, 2), fr(44, 12), fr(10, 3), fr(2, 3))
 
# dictionary of a set of values
# Only the keys are taken in
# consideration by harmonic_mean()
data4 = {1: "one", 2: "two", 3: "three"}
 
# Printing the harmonic mean of above datasets
print("Harmonic Mean of data set 1 is % s"
                 % (harmonic_mean(data1)))
                  
print("Harmonic Mean of data set 2 is % s"
                 % (harmonic_mean(data2)))
 
print("Harmonic Mean of data set 3 is % s"
                 % (harmonic_mean(data3)))
                  
print("Harmonic Mean of data set 4 is % s"
                % (harmonic_mean(data4)))

输出 ：

Harmonic Mean of data set 1 is 4.299197943900386
Harmonic Mean of data set 2 is 4.574783168721765
Harmonic Mean of data set 4 is 55/56
Harmonic Mean of data set 5 is 1.6363636363636365

代码 #3：演示 StatisticsError

Python3

# Python code to demonstrate StatisticsError
# while using harmonic_mean()
 
# importing statistics module
import statistics
 
# data-set of numbers containing
# a negative number
dat1 = [1, -1]
 
# Statistics Error is raised when the
# data-set passed as parameter is
# empty or contain a negative value
print(statistics.harmonic_mean(dat1))

输出 ：

Traceback (most recent call last):
  File "C:/Users/Souveek/PycharmProjects/Test.py", line 12, in 
    print(statistics.harmonic_mean((1, -1)))
  File "C:\Users\Souveek\AppData\Local\Programs\Python\Python36-32\Lib\statistics.py", line 356, in harmonic_mean
    T, total, count = _sum(1/x for x in _fail_neg(data, errmsg))
  File "C:\Users\Souveek\AppData\Local\Programs\Python\Python36-32\Lib\statistics.py", line 148, in _sum
    for n, d in map(_exact_ratio, values):
  File "C:\Users\Souveek\AppData\Local\Programs\Python\Python36-32\Lib\statistics.py", line 356, in 
    T, total, count = _sum(1/x for x in _fail_neg(data, errmsg))
  File "C:\Users\Souveek\AppData\Local\Programs\Python\Python36-32\Lib\statistics.py", line 285, in _fail_neg
    raise StatisticsError(errmsg)
statistics.StatisticsError: harmonic mean does not support negative values

注意：以下代码可能无法在在线 IDE 上运行，因为 Harmonic_mean()函数是 Python3.6 中新引入的应用：
Harmonic Mean 是金融领域的众多重要工具之一（统计下）。加权调和平均是对倍数进行平均的优选方法，例如市盈率 (P/E)，其中价格是分子。它也用于算术平均值高估所需结果的计算中。