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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 )
( Enter your problem )
  1. Mean deviation Introduction
  2. Mean deviation about mean example (Class & Frequency)
  3. Mean deviation about mean example (X & Frequency)
  4. Mean deviation about median example (Class & Frequency)
  5. Mean deviation about median example (X & Frequency)
  6. Mean deviation about mode example (Class & Frequency)
  7. 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-XFrequency
2 - 43
4 - 64
6 - 82
8 - 101


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 - 43 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 - 64 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 - 82 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 - 101 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-XFrequency
10 - 2015
20 - 3025
30 - 4020
40 - 5012
50 - 608
60 - 705
70 - 803


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 - 20151522520300
20 - 30252562510250
30 - 40203570000
40 - 50124554010120
50 - 6085544020160
60 - 7056532530150
70 - 8037522540120
------------------
--`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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1. Mean deviation Introduction
(Previous example)		3. Mean deviation about mean example (X & Frequency)
(Next example)


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