The median of the following data is `50`. Find the values of `p` and `q`, if the sum of the all the frequencies is `90`.

Options

A. `p = 5` `q = 7`
B. `p = 2` `q = 6`
C. `p = 3 ` `q = 5`
D. `p = 5` `q = 8`

Answer

A

Explanation

Given, n=90
`(N)/(2)=(90)/(2)=45`
Which lies in the interval 50-60
Lower limit, l=50,f=20,cf=40+p,h=10
`"Median"=l+(((N)/(2)-cf))/(f)xxh`
`=50+(45-40-p)/(20)xx10`
`Rightarrow 50=50+((5-p)/(2))`
`Rightarrow 0=(5-p)/(2)`
`therefore p=5`
Also, 78+p+q=90
`Rightarrow 78+5+q=90`
`Rightarrow q=90-83`
`therefore q=7`