Calculate the mean deviation about median age for the age distribution of 100 persons given below

Age Number
16-20 5
21-25 6
26-30 12
31-35 14
36-40 26
41-45 12
46-50 16
51-55 9

Asked by Abhisek | 11 months ago |  97

1 Answer

Solution :-

The class interval containing Nth/2 or 50th item is 35.5 – 40.5

So, 35.5 – 40.5 is the median class.

Then,

Median = \( l +\dfrac{\dfrac{N}{2}-C}{f}× h\)

Where, l = 35.5, c = 37, f = 26, h = 5 and N = 100

Median = \( 35.5+\dfrac{50-37}{26}× 5\)

= 35.5 + 2.5

= 38

Thus, mean deviation about the median is given by

\(MD(M) = \dfrac{1}{N} \displaystyle\sum_{i=1}^{8} f_i |X_i-M|\)

\( \dfrac{1}{100}\times 735\)

= 7.35

Answered by Pragya Singh | 11 months ago

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