Harmonic Mean (also known as Contrary mean) is one of several kinds of average and in particular one of the Pythagorean means. Usually used in situations when average rates are desired. The harmonic mean is also the reciprocal of the arithmetic mean of the reciprocals of a given set of observations.
For example, harmonic mean of 1, 4 and 4 can be calculated as :
Harmonic mean can be incorporated in Python3 by using harmonic_mean() function from the statistics module.
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.
Note: Harmonic mean is calculated only using positive values in the list, set, or any sequence.
Code #1 :
Python3
# Python3 code to demonstrate the # working of harmonic_mean() function# Import statistics moduleimport statistics# list of positive real valued numbersdata = [1, 3, 5, 7, 9]# using harmonic mean function to calculate# the harmonic mean of the given data-setprint("Harmonic Mean is % s " % (statistics.harmonic_mean(data))) |
Output :
Harmonic Mean is 2.797513321492007
Code #2 :
Python3
# Python3 program to demonstrate harmonic_mean()# function from the statistics module# Importing the statistics modulefrom statistics import harmonic_mean# Importing fractions module as frfrom fractions import Fraction as fr# tuple of positive integer numbersdata1 = (2, 3, 4, 5, 7, 9, 11)# tuple of a set of floating-point valuesdata2 = (2.4, 5.1, 6.7, 8.9)# tuple of a set of fractional numbersdata3 = (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 datasetsprint("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))) |
Output :
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
Code #3 : Demonstrating StatisticsError
Python3
# Python code to demonstrate StatisticsError# while using harmonic_mean()# importing statistics moduleimport statistics# data-set of numbers containing# a negative numberdat1 = [1, -1]# Statistics Error is raised when the# data-set passed as parameter is # empty or contain a negative valueprint(statistics.harmonic_mean(dat1)) |
Output :
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
Note: Following codes may not run on online IDEs, since the harmonic_mean() function is newly introduced in Python3.6
Applications :
Harmonic Mean is one of the many important tools in finance (under statistics). The weighted harmonic mean is the preferable method for averaging multiples, such as the price–earnings ratio (P/E), in which price is in the numerator. It is also used in calculations in places where the arithmetic mean overestimates the required result.
