This document provides information about calculating the mean absolute deviation and coefficient of dispersion for grouped and ungrouped data: - The mean absolute deviation is the average of the absolute differences between observations and the central value (mean, median or mode). - Formulas are given for calculating the mean absolute deviation about the median for ungrouped and grouped data. - An example shows how to calculate the mean deviation from the median and coefficient of dispersion for a set of ungrouped data and for grouped data from a frequency distribution. - Practice problems are included for the reader to calculate these measures of dispersion.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS

2. Mean Absolute Deviation:
A good measure of dispersion should consider
differences of all observations from the mean. If we
simply average all differences from the mean, the
positives and the negatives will cancel out, even though
they both contribute to dispersion, and the resulting
average will equal zero. The mean absolute
deviation (MAD) is an average of the absolute
differences between the observations and central value
such as mean median or mode.

3. Formula Mean Absolute Deviation about median:
. ( ) for ungrouped data
x x
M D x
n


 %
%
. ( ) for grouped data
f x x
M D x
f




%
%
x%
 . x
100
x
M D
 
%
%Coefficient of Mean Deviation( )

4. Example-1: Calculate mean deviation about median and coefficient of Dispersion.
2, 6, 4, 8, 10
Solution: First arrange the data and find median
2, 4, 6, 8, 10
n = 5
5 1
2
3
6
the value
rd value
x
 
  
 

%

5. X
2
4
6
8
10
x~x 
462 
264 
066 
268 
4610 
12x~x 
 
%40
100
6
4.2
100
x~
)x~(D.M
DispersionoftCoefficien
4.2
5
12
n
x~x
x~D.M







6. DO YOURSELF
1-For the following data
6, 12, 18, 24, 30
(i)Calculate mean absolute deviation about median.
(ii) Calculate coefficient of dispersion.(7.2, 40%)
2- For the following set of data
7, 2, 9, 11, 12, 4, 5, 1
(i)Calculate mean absolute deviation about median.
(ii) Calculate coefficient of dispersion.(3.375, 56.25%)

7. C.B. F c.f x f
2 – 4 2 2 3 3.7 7.4
4 – 6 3 5 5 1.7 5.1
6 – 8 6 11 7 0.3 1.8
8 – 10 2 13 9 2.3 4.6
10 –
12
1 14 11 4.3 4.3
x~x x~x 
14f  2.23x~xf 
Example-2: Calculate Mean deviation from median and coefficient of Dispersion.
First find median

8. 14
7 6 8
2 2
For median
f
th lie in

  
6
8 6 2
6
. 5
l
h
f
c f

  


 
 
. .
2
2
6 7 5 6.7
6
23.2
. 1.66
14
. ( )
100
1.66
= 24.78%
6.7
h f
x L c f
f
x
f x x
M D x
f
M D x
Coefficient of Dispersion
x
 
    
   
 
  

 


%
%
%
%
%
%

9. C.I 4 – 6 7 – 9 10 – 12 13 – 15 16 – 18
F 2 8 10 6 4
DO YOURSELF
1-From the following frequency distribution
(i)Calculate mean absolute deviation about median.(2.6)
(ii) Calculate coefficient of dispersion.(23.64%)
2- From the following distribution:
(i)Calculate mean absolute deviation about median.(27.29)
(ii) Calculate coefficient of dispersion.(29.62%)
Groups 0 – 10 10 – 40 40 – 90 90 – 100 100 – 105 105 – 120 120 - 140
f 50 100 140 210 100 50 20