Mean deviation about mean example (Class & Frequency) for grouped data

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Home > Statistical Methods calculators > Mean deviation about mean for grouped data example

Mean deviation about mean example (Class & Frequency) for grouped data ( Enter your problem )

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Mean deviation Introduction
Mean deviation about mean example (Class & Frequency)
Mean deviation about mean example (X & Frequency)
Mean deviation about median example (Class & Frequency)
Mean deviation about median example (X & Frequency)
Mean deviation about mode example (Class & Frequency)
Mean deviation about mode example (X & Frequency)

1. Mean deviation Introduction
(Previous example)

3. Mean deviation about mean example (X & Frequency)
(Next example)

2. Mean deviation about mean example (Class & Frequency)

Formula

1. Mean deviation of mean `delta bar x = (sum f*|x - bar x|)/n`

2. Mean deviation of median `delta M = (sum f*|x - M|)/n`

3. Mean deviation of mode `delta Z = (sum f*|x - Z|)/n`

Examples
1. Calculate Mean deviation about mean from the following grouped data
Class-X Frequency
2 - 4 3
4 - 6 4
6 - 8 2
8 - 10 1

Solution:
Mean `bar x=(sum f x)/(sum f)`

`=52/10`

`=5.2`

Class `(1)`	`f` `(2)`	Mid value (`x`) `(3)`	`f*x` `(4)=(2)xx(3)`	`\|x-bar x\|=\|x-5.2\|` `(5)`	`f*\|x-bar x\|` `(6)=(2)xx(5)`
2 - 4	3	3 `3=(2+4)/2`	9 `9=3xx3` `(4)=(2)xx(3)`	2.2 `\|3-5.2\|=2.2` `\|x - 5.2\|`	6.6 `6.6=3xx2.2` `(6)=(2)xx(5)`
4 - 6	4	5 `5=(4+6)/2`	20 `20=4xx5` `(4)=(2)xx(3)`	0.2 `\|5-5.2\|=0.2` `\|x - 5.2\|`	0.8 `0.8=4xx0.2` `(6)=(2)xx(5)`
6 - 8	2	7 `7=(6+8)/2`	14 `14=2xx7` `(4)=(2)xx(3)`	1.8 `\|7-5.2\|=1.8` `\|x - 5.2\|`	3.6 `3.6=2xx1.8` `(6)=(2)xx(5)`
8 - 10	1	9 `9=(8+10)/2`	9 `9=1xx9` `(4)=(2)xx(3)`	3.8 `\|9-5.2\|=3.8` `\|x - 5.2\|`	3.8 `3.8=1xx3.8` `(6)=(2)xx(5)`
---	---	---	---	---	---
--	`n=10`	--	`sum f*x=52`	--	`sum f*\|x-bar x\|=14.8`

Mean deviation of Mean
`delta bar x = (sum f*|x - bar x|)/n`

`delta bar x = 14.8/10`

`delta bar x = 1.48`

Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=1.48/5.2`

`=0.28`

2. Calculate Mean deviation about mean from the following grouped data
Class-X Frequency
10 - 20 15
20 - 30 25
30 - 40 20
40 - 50 12
50 - 60 8
60 - 70 5
70 - 80 3

Solution:
Mean `bar x=(sum f x)/(sum f)`

`=3080/88`

`=35`

Class `(1)`	`f` `(2)`	Mid value (`x`) `(3)`	`f*x` `(4)=(2)xx(3)`	`\|x-bar x\|=\|x-35\|` `(5)`	`f*\|x-bar x\|` `(6)=(2)xx(5)`
10 - 20	15	15	225	20	300
20 - 30	25	25	625	10	250
30 - 40	20	35	700	0	0
40 - 50	12	45	540	10	120
50 - 60	8	55	440	20	160
60 - 70	5	65	325	30	150
70 - 80	3	75	225	40	120
---	---	---	---	---	---
--	`n=88`	--	`sum f*x=3080`	--	`sum f*\|x-bar x\|=1100`

Mean deviation of Mean
`delta bar x = (sum f*|x - bar x|)/n`

`delta bar x = 1100/88`

`delta bar x = 12.5`

Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=12.5/35`

`=0.3571`

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