1. Calculate Geometric mean from the following grouped data

X	Frequency
1	5
2	10
3	6
4	3
5	2

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`

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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`

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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`

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