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Question

Calculate mean deviation from the following data, using mean and median, respectively.
Size 4 6 8 10 12 14 16
Frequency 2 4 5 3 2 1 4

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Solution

Calculation of mean deviation from median
Size (X) Frequency (f) Cumulative frequency (c.f.) Deviation from median
|dM| = |X − M|
M = 8
f|dM|
4
6
8
10
12
14
16
2
4
5
3
2
1
4
2
2 + 4 = 6
6 + 5 = 11
11 + 3 = 14
14 + 2 = 16
16 + 1 = 17
17 = 4 = 21
4
2
0
2
4
6
8
8
8
0
6
8
6
32
Σf=N= 21 Σf|dM| = 68

(a) Median or (M) = Size of N+12th item
= Size of 21+12th item
= Size of 11th item
= 8

(b) Mean Deviation from median

MDM=ΣfdMN=6821=3.24

Calculation of mean deviation from mean
Size (X) Frequency (f) fX From mean deviation from mean
dX=X-XX=9.71
fdX¯
4
6
8
10
12
14
16
2
4
5
3
2
1
4
8
24
40
30
24
14
64
5.71
3.71
1.71
0.29
2.29
4.29
6.29
11.42
14.84
8.55
0.87
4.58
4.29
25.16
Σf = 21 ΣfX = 204 ΣfdX¯= 69.71

(a) Mean (X¯)=ΣfXΣf=20421=9.71

(b) Mean deviation from A.M.

MDX=ΣfdXΣf=69.7121=3.32

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