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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for grouped data example
Mean deviation, Coefficient of Mean deviation Example for grouped data ( Enter your problem )
( Enter your problem )
  1. Mean deviation, Coefficient of Mean deviation Example
  2. Quartile deviation, Coefficient of Quartile deviation Example
  3. Decile deviation, Coefficient of Decile deviation Example
  4. Percentile deviation, Coefficient of Percentile deviation Example
 		Other related methods
  1. Mean, Median and Mode
  2. Quartile, Decile, Percentile, Octile, Quintile
  3. Population Variance, Standard deviation and coefficient of variation
  4. Sample Variance, Standard deviation and coefficient of variation
  5. Population Skewness, Kurtosis
  6. Sample Skewness, Kurtosis
  7. Geometric mean, Harmonic mean
  8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
  9. Five number summary
  10. Box and Whisker Plots
  11. Mode using Grouping Method
  12. Less than type Cumulative frequency table
  13. More than type Cumulative frequency table
  14. Class and their frequency table
7. Geometric mean, Harmonic mean
(Previous method)		2. Quartile deviation, Coefficient of Quartile deviation Example
(Next example)

1. Mean deviation, Coefficient of Mean deviation Example


1. Calculate Mean deviation from the following grouped data
XFrequency
01
15
210
36
43


Solution:
Mean deviation :
`x`
`(1)`		`f`
`(2)`		`f*x`
`(3)=(2)xx(1)`		`|x-bar x|=|x-2.2|`
`(4)`		`f*|x-bar x|`
`(5)=(2)xx(4)`
0102.22.2
1551.26
210200.22
36180.84.8
43121.85.4
---------------
--`n=25``sum f*x=55`--`sum f*|x-bar x|=20.4`


Mean `bar x=(sum f x)/n`

`=55/25`

`=2.2`

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

`delta bar x = 20.4/25`

`delta bar x = 0.816`


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

`=0.816/2.2`

`=0.3709`

2. Calculate Mean deviation from the following grouped data
XFrequency
103
1112
1218
1312
143


Solution:
Mean deviation :
`x`
`(1)`		`f`
`(2)`		`f*x`
`(3)=(2)xx(1)`		`|x-bar x|=|x-12|`
`(4)`		`f*|x-bar x|`
`(5)=(2)xx(4)`
1033026
1112132112
121821600
1312156112
1434226
---------------
--`n=48``sum f*x=576`--`sum f*|x-bar x|=36`


Mean `bar x=(sum f x)/n`

`=576/48`

`=12`

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

`delta bar x = 36/48`

`delta bar x = 0.75`


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

`=0.75/12`

`=0.0625`

3. Calculate Mean deviation from the following grouped data
ClassFrequency
2 - 43
4 - 64
6 - 82
8 - 101


Solution:
Mean deviation :
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 - 43392.26.6
4 - 645200.20.8
6 - 827141.83.6
8 - 101993.83.8
------------------
--`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`

`=0.2846`

4. Calculate Mean deviation from the following grouped data
ClassFrequency
0 - 25
2 - 416
4 - 613
6 - 87
8 - 105
10 - 124


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

`=256/50`

`=5.12`

Class
`(1)`		`f`
`(2)`		Mid value (`x`)
`(3)`		`f*x`
`(4)=(2)xx(3)`		`|x-bar x|=|x-5.12|`
`(5)`		`f*|x-bar x|`
`(6)=(2)xx(5)`
0 - 25154.1220.6
2 - 4163482.1233.92
4 - 6135650.121.56
6 - 877491.8813.16
8 - 1059453.8819.4
10 - 12411445.8823.52
------------------
--`n=50`--`sum f*x=256`--`sum f*|x-bar x|=112.16`


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

`delta bar x = 112.16/50`

`delta bar x = 2.2432`


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

`=2.2432/5.12`

`=0.4381`

This material is intended as a summary. Use your textbook for detail explanation.
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7. Geometric mean, Harmonic mean
(Previous method)		2. Quartile deviation, Coefficient of Quartile deviation Example
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