1. Calculate Geometric mean from the following grouped data
Solution:
Geometric mean :
| `x` | `f` | `flog(x)` |
| 1 | 5 | 0 |
| 2 | 10 | 3.0103 |
| 3 | 6 | 2.8627 |
| 4 | 3 | 1.8062 |
| 5 | 2 | 1.3979 |
| --- | --- | --- |
| -- | `n=26` | `sum flog(x)=9.0771` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((9.0771)/(26))`
`= Antilog(0.3491)`
`= 2.2342`
2. Calculate Geometric mean from the following grouped data
| Class | Frequency |
| 2 - 4 | 3 |
| 4 - 6 | 4 |
| 6 - 8 | 2 |
| 8 - 10 | 1 |
Solution:
Geometric mean :
| Class | Mid value (`x`)
`(2)` | `f` | `flog(x)` |
| 2 - 4 | 3 | 3 | 1.4314 |
| 4 - 6 | 5 | 4 | 2.7959 |
| 6 - 8 | 7 | 2 | 1.6902 |
| 8 - 10 | 9 | 1 | 0.9542 |
| --- | --- | --- | --- |
| -- | -- | `n=10` | `sum flog(x)=6.8717` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((6.8717)/(10))`
`= Antilog(0.6872)`
`= 4.866`
3. Calculate Geometric 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:
Geometric mean :
| Class | Mid value (`x`)
`(2)` | `f` | `flog(x)` |
| 0 - 2 | 1 | 5 | 0 |
| 2 - 4 | 3 | 16 | 7.6339 |
| 4 - 6 | 5 | 13 | 9.0866 |
| 6 - 8 | 7 | 7 | 5.9157 |
| 8 - 10 | 9 | 5 | 4.7712 |
| 10 - 12 | 11 | 4 | 4.1656 |
| --- | --- | --- | --- |
| -- | -- | `n=50` | `sum flog(x)=31.573` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((31.573)/(50))`
`= Antilog(0.6315)`
`= 4.2802`
This material is intended as a summary. Use your textbook for detail explanation.
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