Harmonic Mean Calculator

Dataset set
comma separated input values
Number of samples  =  5
Harmonic mean  =  9.5238

Harmonic Mean - work with steps

Input Data :
Data set = 5, 8, 12, 15, 20
Total number of elements = 5

Objective :
Find what is harmonic mean value for given input data?

Formula :
Harmonic Mean Formula

Solution :
Harmonic mean = 51/5 + 1/ 8 + 1/ 12 + 1/ 15 + 1/ 20
= 50.2 + 0.125 + 0.0833 + 0.0667 + 0.05
= 50.525
Harmonic mean = 9.5238

Harmonic Mean Calculator is an online statistics tool programmed to calculate Harmonic Mean from the number of observations, divided by the sum of reciprocals of the observations. The harmonic mean is one of the three Pythagorean means, involving in many situations where rates, ratios, geometry, trigonometry etc considered, the harmonic mean provides the truest average.

Definition - Harmonic Mean

Harmonic Mean is the reciprocal of the arithmetic mean of the reciprocals. In other words, it is the number of observations, divided by the sum of reciprocals of the observations. This is also is one of several kinds of average and it is appropriate for situations when the average of rates is desired.

Harmonic Mean Formula

The harmonic mean H of the positive real numbers x1, x2, x3, ...xn > 0 can be derived from the formula
Harmonic Mean Formula

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. With this online harmonic mean calculator you can effortlessly make your calculation for the set of given observations