Examples
1. Calculate Geometric mean, Harmonic mean from the following grouped data
| Class | Frequency |
| 2 - 4 | 3 |
| 4 - 6 | 4 |
| 6 - 8 | 2 |
| 8 - 10 | 1 |
Solution:
Geometric mean,Harmonic mean :
| Class | Mid value (`x`)
`(2)` | `f` | `flog(x)` | `f/x` |
| 2 - 4 | 3 | 3 | 1.4314 | 1 |
| 4 - 6 | 5 | 4 | 2.7959 | 0.8 |
| 6 - 8 | 7 | 2 | 1.6902 | 0.2857 |
| 8 - 10 | 9 | 1 | 0.9542 | 0.1111 |
| --- | --- | --- | --- | --- |
| -- | -- | `n=10` | `sum flog(x)=6.8717` | `sum (f/x)=2.1968` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((6.8717)/(10))`
`= Antilog(0.6872)`
`= 4.866`
HM of X `= n/(sum (f/x))`
`=(10)/(2.1968)`
`=4.552`
2. Calculate Geometric mean, Harmonic mean from the following grouped data
| X | Frequency |
| 10 | 3 |
| 11 | 12 |
| 12 | 18 |
| 13 | 12 |
| 14 | 3 |
Solution:
Geometric mean,Harmonic mean :
| `x` | `f` | `flog(x)` | `f/x` |
| 10 | 3 | 3 | 0.3 |
| 11 | 12 | 12.4967 | 1.0909 |
| 12 | 18 | 19.4253 | 1.5 |
| 13 | 12 | 13.3673 | 0.9231 |
| 14 | 3 | 3.4384 | 0.2143 |
| --- | --- | --- | --- |
| -- | `n=48` | `sum flog(x)=51.7277` | `sum (f/x)=4.0283` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((51.7277)/(48))`
`= Antilog(1.0777)`
`= 11.958`
HM of X `= n/(sum (f/x))`
`=(48)/(4.0283)`
`=11.9158`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
