Program for harmonic mean of numbers

Given an array of elements, find harmonic mean of numbers. 
Examples: 
 

Input : arr[] = {2.0, 1.0}
Output : 1.3333
Harmonic mean = 2/(1/2.0 + 1/1.0)
 = (2 * 2)/3
 = 1.333

Input : arr[] = {13.5, 14.5, 14.8, 15.2, 16.1}
Output : 14.7707

 

Harmonic mean is used when average of rates is required, below is the formula.
Harmonic mean of n numbers x₁, x₂, 
x₃, . . ., x_n can written as below.
Harmonic mean = n / ((1/x₁) + (1/x₂) + (1/x₃) + . . . + (1/x_n))

 
Below is the implementation of Harmonic Mean. 
 

Output: 

14.7707

Time Complexity: O(n)

Auxiliary Space: O(1), since no extra space has been taken.
What if we are given elements and their frequencies? 
If we are given n numbers and every number has some frequency then simply we use formula 
Harmonic mean = (Frequency-Sum) /((f₁/x₁) + (f₂/x₂) + (f₃/x₃) + . . . + (f_n/x_n)) 
Where f₁, f₂, f₃, . . ., f_n are the frequencies of elements and x₁, ₂, x₃, . . ., x_n are the elements of array.
Frequency-Sum = f₁ + f₂ + f₃, . . ., f_n
Examples: 
 

Input : num[] = {13, 14, 15, 16, 17}
 freq[] = {2, 5, 13, 7, 3}
Output : 15.0631

 

Output: 

15.0631

Time Complexity: O(n)

Auxiliary Space: O(1)
Harmonic mean of numbers using harmonic_mean() in Python: 
Simple Python program to find harmonic mean using harmonic_mean() function. 
 

Output: 14.770680729373778

Time Complexity: O(n)

Auxiliary Space: O(1)