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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`

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

`=(10)/(2.1968)`

`=4.552`

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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`

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

`=(48)/(4.0283)`

`=11.9158`

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