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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`

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HM of X `= (sum f)/(sum (f/x))`

`=(7)/(1.5178)`

`=4.6118`

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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`

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HM of X `= (sum f)/(sum (f/x))`

`=(10)/(0.1154)`

`=86.6251`

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