Statistics - Harmonic Mean of Continous 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

In case of continous series, a mid point is computed as $\frac{lower-limit + upper-limit}{2}$ and Harmonic Mean is computed using following formula.

Formula

$H.M. = \frac{N}{\sum (\frac{f}{m})}$

Where −

Problem Statement:

Calculate Harmonic Mean for the following continous data:

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

Solution:

Based on the given data, we have:

Items	Mid-pt m	Frequency f	${\frac{f}{m}}$
0-10	5	2	0.4000
10-20	15	5	0.3333
20-30	25	1	0.0400
30-40	35	3	0.0857
		N=11	0.8590

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

$H.M. = \frac{N}{\sum (\frac{f}{m})} \\[7pt] \, = \frac{11}{0.8590} \\[7pt] \, = 12.80$

The Harmonic Mean of the given numbers is 12.80.