# Statistics - Harmonic Mean of Continous Series

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

 Items Frequency 0-5 5-10 10-20 20-30 30-40 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 −

• ${H.M.}$ = Harmonic Mean

• ${N}$ = Number of observations.

• ${m}$ = Mid Point of observation.

• ${f}$ = Frequency of variable X

### Example

Problem Statement:

Calculate Harmonic Mean for the following continous data:

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

Solution:

Based on the given data, we have:

ItemsMid-pt
m
Frequency
f
${\frac{f}{m}}$
0-10520.4000
10-201550.3333
20-302510.0400
30-403530.0857
N=110.8590

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.