Look at the frequency distribution table given below:

$\begin{matrix} C l a s s i n t e r v a l & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 F r e q u e n c y & 8 & 12 & 20 & 10 \end{matrix}$

The median of the above distribution is

(a) 56.5 (b) 57.5 (c) 58.5 (d) 59

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Solution

Class Frequency Cumulattive frequency

35-45 8 8

45-55 12 20

55-65 20 40

65-75 10 50

$N equals 50 rightwards double arrow N over 2 equals 25M e d i a n space c l a s s equals 55 minus 65H e r e comma l equals 55 comma f equals 20 comma F equals 20 comma h equals 10M e d i a n equals l plus open parentheses fraction numerator begin display style N over 2 end style minus F over denominator f end fraction close parentheses cross times hspace space space space space space space space space space space space equals 55 plus open parentheses fraction numerator 25 minus 20 over denominator 20 end fraction close parentheses cross times 10space space space space space space space space space space space space space equals 55 plus 5 over 20 cross times 10space space space space space space space space space space space space space equals 57.5O p t i o n space bspace space space space space space space space space space space space space space$

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Class interval	35-45	45-55	55-65	65-75
Frequency	8	12	20	10

9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9

12

Age in years	No. of persons
Above 108 Above 96 Above 84 Above 72 Above 60 Above 48 Above 36 Above 24 Above 12 Above 0	0 1 3 5 20 158 427 809 1026 1124

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