# Statistics – Harmonic Mean

## What is Harmonic Mean?

Harmonic Mean is also a mathematical average but is limited in its application. It is generally used to find average of variables that are expressed as a ratio of two different measuring units e. g. speed is measured in km/hr or miles/sec etc.

## Formula

H.M.=W∑(WX)H.M.=W∑(WX)

Where −

·        H.M.H.M. = Harmonic Mean

·        WW = Weight

·        XX = Variable value

### Example

Problem Statement:

Find the weighted H.M. of the items 4, 7,12,19,25 with weights 1, 2,1,1,1 respectively.

Solution:

Based on the above mentioned formula, Harmonic Mean G.M.G.M. will be:

H.M.=W∑(WX)=60.7116=8.4317H.M.=W∑(WX)=60.7116=8.4317

∴ Weighted H.M = 8.4317

We’re going to discuss methods to compute the Harmonic Mean for three types of series:

·        Individual Data Series

·        Discrete Data Series

·        Continuous Data Series

## Individual Data Series

When data is given on individual basis. Following is an example of individual series:

## Discrete Data Series

When data is given alongwith their frequencies. Following is an example of discrete series:

## Continuous Data Series

When data is given based on ranges alongwith their frequencies. Following is an example of continous series: