Consider the following table:

$\begin{matrix} C l a s s i n t e r v a l & 10 - 14 & 14 - 18 & 18 - 22 & 22 - 26 & 26 - 30 F r e q u e n c y & 5 & 11 & 16 & 25 & 19 \end{matrix}$

The mode of the above data is

(a) 23.5 (b) 24 (c) 24.4 (d) 25

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Solution

Class Frequency Cumulative frequency

10-14 5 5

14-18 11 16

18-22 16 32

22-26 25 57

26-30 19 76

$N over 2 equals 76 over 2 equals 38 M o d a l space c l a s s equals 22 minus 26 l equals 22 comma f equals 25 comma f subscript 1 equals 16 comma f subscript 2 equals 19 comma h equals 4 M o d e equals l plus fraction numerator f minus f subscript 1 over denominator 2 f minus f subscript 1 minus f subscript 2 end fraction cross times h space space space space space space space space equals 22 plus fraction numerator 25 minus 16 over denominator 2 cross times 25 minus 16 minus 19 end fraction cross times 4 space space space space space space space space equals 22 plus 9 over 15 cross times 4 space space space space space space space space space equals 22 plus 2.4 space space space space space space space space space space equals 24.4 O p t i o n space C$

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