Statistics - Harmonic Mean of Discrete 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

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 14 36 45 70 105
Frequency 2 5 1 3 2

Solution:

Based on the given data, we have:

${x}$ ${f}$ ${\frac{f}{X}}$
14 2 0.1428
36 5 0.1388
45 1 0.0222
70 3 0.0428
105 2 0.0190
Total 0.3656

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.

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