1. Calculate Harmonic mean from the following grouped data
Solution:
Harmonic mean :
| `x` | `f` | `f/x` |
| 1 | 5 | 5 |
| 2 | 10 | 5 |
| 3 | 6 | 2 |
| 4 | 3 | 0.75 |
| 5 | 2 | 0.4 |
| --- | --- | --- |
| -- | `n=26` | `sum (f/x)=13.15` |
HM of X `= n/(sum (f/x))`
`=(26)/(13.15)`
`=1.9772`
2. Calculate Harmonic mean from the following grouped data
| Class | Frequency |
| 2 - 4 | 3 |
| 4 - 6 | 4 |
| 6 - 8 | 2 |
| 8 - 10 | 1 |
Solution:
Harmonic mean :
| Class | Mid value (`x`)
`(2)` | `f` | `f/x` |
| 2 - 4 | 3 | 3 | 1 |
| 4 - 6 | 5 | 4 | 0.8 |
| 6 - 8 | 7 | 2 | 0.2857 |
| 8 - 10 | 9 | 1 | 0.1111 |
| --- | --- | --- | --- |
| -- | -- | `n=10` | `sum (f/x)=2.1968` |
HM of X `= n/(sum (f/x))`
`=(10)/(2.1968)`
`=4.552`
3. Calculate Harmonic mean from the following grouped data
| Class | Frequency |
| 0 - 2 | 5 |
| 2 - 4 | 16 |
| 4 - 6 | 13 |
| 6 - 8 | 7 |
| 8 - 10 | 5 |
| 10 - 12 | 4 |
Solution:
Harmonic mean :
| Class | Mid value (`x`)
`(2)` | `f` | `f/x` |
| 0 - 2 | 1 | 5 | 5 |
| 2 - 4 | 3 | 16 | 5.3333 |
| 4 - 6 | 5 | 13 | 2.6 |
| 6 - 8 | 7 | 7 | 1 |
| 8 - 10 | 9 | 5 | 0.5556 |
| 10 - 12 | 11 | 4 | 0.3636 |
| --- | --- | --- | --- |
| -- | -- | `n=50` | `sum (f/x)=14.8525` |
HM of X `= n/(sum (f/x))`
`=(50)/(14.8525)`
`=3.3664`
This material is intended as a summary. Use your textbook for detail explanation.
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