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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 −
${H.M.}$ = 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 | 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.
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