In the given table, frequency distribution of marks obtained by the stubents in a question paper of mathematics are given below

Then, median of marks is

Options

A. `27.7`
B. 25
C. `17.3`
D. 9

Answer

A

Explanation

`N = sum f = 5 + 6 + 9 + 12 + 4 = 36`
`(N + 1)/( 2) = ( 36 + 1)/( 2) ` = 18 . 5 which lies in the cumulative frequency of third class interval . Hence third class interval (20 - 30) is median class
Formula for median class,
`M_(d) = L_(l) + ((N)/(2)-F)/(f_(m) ) xx i `
`L_(i)` = Lower limit of median class = 20
`f_(m)` = Frequency of median class = 9
Cumulative frequency before the median class = 5 + 6 = 11
` i = 30 - 20 = 10, N = sum f = 36`
` M_(d) = 20 + (18 - 11)/( 9) xx 10`
` = 20 + (70)/( 9) = 20 + 7 . 70 = 27 . 70`