Compute the median from the following table

Options

A. `36.55`
B. `35.55`
C. `40.05`
D. None of these

Answer

A

Explanation

`N=sum f=159` (Odd number)
Median is `(1)/(2)(n+1)=(1)/(2)(159+1)=80`th value, which lies in the class 30-40 (see the row of cumulative frequency 95, which contains 80).
Hence median class is 30-40.
`therefore` We have
l=Lower limit of median class=30
f=Frequency of median class=45
C=Total of all frequencies preceding median class=50
i=Width of class interval of median class=10
`therefore` Required median `=l+((N)/(2)-C)/(f)xxi=30+((159)/(2)-50)/(45)xx10`
`=30+(295)/(45)=36.55`