Examples
1. Calculate Geometric mean, Harmonic mean from the following data
3,13,11,15,5,4,2
Solution:
| `x` | `log(x)` | `1/x` |
| 3 | 1.0986 | 0.3333 |
| 13 | 2.5649 | 0.0769 |
| 11 | 2.3979 | 0.0909 |
| 15 | 2.7081 | 0.0667 |
| 5 | 1.6094 | 0.2 |
| 4 | 1.3863 | 0.25 |
| 2 | 0.6931 | 0.5 |
| --- | --- | --- |
| `sum log(x)=12.4584` | `sum 1/x=1.5178` |
GM of X `= Antilog((sum flog(x))/(sum f))`
`= Antilog((12.4584)/(7))`
`= Antilog(1.7798)`
`= 5.9285`
HM of X `= (sum f)/(sum (f/x))`
`=(7)/(1.5178)`
`=4.6118`
2. Calculate Geometric mean, Harmonic mean from the following data
85,96,76,108,85,80,100,85,70,95
Solution:
| `x` | `log(x)` | `1/x` |
| 85 | 4.4427 | 0.0118 |
| 96 | 4.5643 | 0.0104 |
| 76 | 4.3307 | 0.0132 |
| 108 | 4.6821 | 0.0093 |
| 85 | 4.4427 | 0.0118 |
| 80 | 4.382 | 0.0125 |
| 100 | 4.6052 | 0.01 |
| 85 | 4.4427 | 0.0118 |
| 70 | 4.2485 | 0.0143 |
| 95 | 4.5539 | 0.0105 |
| --- | --- | --- |
| `sum log(x)=44.6947` | `sum 1/x=0.1154` |
GM of X `= Antilog((sum flog(x))/(sum f))`
`= Antilog((44.6947)/(10))`
`= Antilog(4.4695)`
`= 87.3107`
HM of X `= (sum f)/(sum (f/x))`
`=(10)/(0.1154)`
`=86.6251`
This material is intended as a summary. Use your textbook for detail explanation.
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