Harmonic mean Example for grouped data

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Harmonic mean Example for grouped data ( Enter your problem )

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Formula & Example
Geometric mean Example
Harmonic mean Example

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2. Geometric mean Example
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3. Harmonic mean Example

1. Calculate Harmonic mean from the following grouped data
X Frequency
1 5
2 10
3 6
4 3
5 2

Solution:
Harmonic mean :

`x`	`f`	`f/x`
1	5	5
2	10	5
3	6	2
4	3	0.75
5	2	0.4
---	---	---
--	`n=26`	`sum (f/x)=13.15`

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

`=(26)/(13.15)`

`=1.9772`

2. Calculate Harmonic mean from the following grouped data
Class Frequency
2 - 4 3
4 - 6 4
6 - 8 2
8 - 10 1

Solution:
Harmonic mean :

Class	Mid value (`x`) `(2)`	`f`	`f/x`
2 - 4	3	3	1
4 - 6	5	4	0.8
6 - 8	7	2	0.2857
8 - 10	9	1	0.1111
---	---	---	---
--	--	`n=10`	`sum (f/x)=2.1968`

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

`=(10)/(2.1968)`

`=4.552`

3. Calculate Harmonic 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:
Harmonic mean :

Class	Mid value (`x`) `(2)`	`f`	`f/x`
0 - 2	1	5	5
2 - 4	3	16	5.3333
4 - 6	5	13	2.6
6 - 8	7	7	1
8 - 10	9	5	0.5556
10 - 12	11	4	0.3636
---	---	---	---
--	--	`n=50`	`sum (f/x)=14.8525`

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

`=(50)/(14.8525)`

`=3.3664`

This material is intended as a summary. Use your textbook for detail explanation.
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