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

Method and examples
Find Mean Deviation(M.D.) about Mean, Median, Mode for grouped data
Type your data in either horizontal or verical format,

OR
X & Frequency   Class & Frequency
Rows :
ClassFrequency
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Mean deviation about Mean
Mean deviation about Median
Mean deviation about Mode 
Decimal Place =
SolutionHelp
Mean deviation about mean for grouped data calculator
1.Calculate mean deviation about mean for the following distribution.
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No. of student 6 5 8 15 7 6 3

2. Calculate mean deviation about median for the following distribution.
Class 1-3 3-5 5-7 7-9 9-11 11-13 13-15 15-17
Frequency 6 53 85 56 21 26 4 4

3. Calculate mean deviation about median for the following distribution.
Class 3-4.9 5-6.9 7-8.9 9-10.9 11-12.9 13-14.9 15-16.9
Frequency 5 8 30 82 45 24 6

4. Calculate mean deviation about median for the following distribution.
x 0 1 2 3 4 5 6 7 8 9 10 11 12
f 15 16 21 10 17 8 4 2 1 2 2 0 2


Example
1. Calculate Mean deviation about mean from the following grouped data
Class-XFrequency
2 - 43
4 - 64
6 - 82
8 - 101


Solution:
Mean ˉx=fxf

=5210

=5.2

Class
(1)
f
(2)
Mid value (x)
(3)
fx
(4)=(2)×(3)
|x-ˉx|=|x-5.2|
(5)
f|x-ˉx|
(6)=(2)×(5)
2 - 43 3 3=2+42 9 9=3×3
(4)=(2)×(3)
 2.2 |3-5.2|=2.2
|x-5.2|
 6.6 6.6=3×2.2
(6)=(2)×(5)
4 - 64 5 5=4+62 20 20=4×5
(4)=(2)×(3)
 0.2 |5-5.2|=0.2
|x-5.2|
 0.8 0.8=4×0.2
(6)=(2)×(5)
6 - 82 7 7=6+82 14 14=2×7
(4)=(2)×(3)
 1.8 |7-5.2|=1.8
|x-5.2|
 3.6 3.6=2×1.8
(6)=(2)×(5)
8 - 101 9 9=8+102 9 9=1×9
(4)=(2)×(3)
 3.8 |9-5.2|=3.8
|x-5.2|
 3.8 3.8=1×3.8
(6)=(2)×(5)
------------------
--n=10--fx=52--f|x-ˉx|=14.8


Mean deviation of Mean
δˉx=f|x-ˉx|n

δˉx=14.810

δˉx=1.48


Coefficient of Mean deviation =δˉxˉx

=1.485.2

=0.28




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