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.

Weighted Harmonic Mean

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:

XX	WW	WXWX
4	1	0.2500
7	2	0.2857
12	1	0.0833
19	1	0.0526
25	1	0.0400
	∑W∑W	∑WX∑WX= 0.7116

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:

Items

5

10

20

30

40

50

60

70

Discrete Data Series

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

Items	5	10	20	30	40	50	60	70
Frequency	2	5	1	3	12	0	5	7

Continuous Data Series

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

Items	0-5	5-10	10-20	20-30	30-40
Frequency	2	5	1	3	12