# Statistics - Harmonic Mean of Discrete Series

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

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

In case of discrete series, Harmonic Mean is computed using following formula.

## Formula

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

Where −

• ${H.M.}$ = Harmonic Mean

• ${N}$ = Number of observations.

• ${X}$ = Variable value

• ${f}$ = Frequency of variable X

### Example

Problem Statement:

Calculate Harmonic Mean for the following discrete data:

 Items Frequency 14 36 45 70 105 2 5 1 3 2

Solution:

Based on the given data, we have:

${x}$${f}$${\frac{f}{X}}$
1420.1428
3650.1388
4510.0222
7030.0428
10520.0190
Total0.3656

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

$H.M. = \frac{N}{\sum (\frac{f}{X})} \\[7pt] \, = \frac{5}{0.3656} \\[7pt] \, = 13.67$

The Harmonic Mean of the given numbers is 13.67.