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Question

Find out the average deviation from median for the following distribution:
Values : 6 12 18 24 30 36 42
Frequency : 4 7 9 18 15 10 5

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Solution

Value
(X)
Frequency
(f)
c.f Deviation from Median
|DM|=|X−M|
(M = 24)
f|DM|
6 4 4 18 72
12 7 11 12 84
18 9 20 6 54
24 18 38 0 0
30 15 53 6 90
36 10 63 12 120
42 5 68 18 90
Σf = N = 68 Σf|dm| = 510

Median=Size of N+12th item =Size of 68+12th item =34.5th item
This corresponds to value 24. Thus, median is 24.
Mean deviation from Median=ΣfDMΣf=51068=7.5

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