The mean of the distribution is `50.`

Find the value of `a` and hence the frequencies of `30` and `70`

Options

A. `3`
B. `4`
C. `5`
D. `6`

Answer

C

Explanation

We know that,
Mean of the distribution `(barx)= (underset(i=1)overset(5)Sigmaf_(i)x_(i))/(underset(i=1)overset(5)Sigmaf_(i))=50` (Given)
`rArr (f_(1)x_(1) + f_(2)x_(2)+f_(3)x_(3)+f_(4)x_(4)+f_(5)x_(5))/(f_(1)+f_(2)+f_(3)+f_(4)+f_(5)) = 50`
`rArr ((17)(10) + (5a+a)(30)+(32)(50)+(7a-11)(70)+(19)(90))/(12a+60)=50`
`rArr (3570-770+640a)/(12a+60)=50`
`rArr 2800 + 640a = 600a +300)`
`rArr 40a=200 rArr a=5)`
`therefore` Frequency of `30 = 5a+3=5(5)+3 (put a=5) `
`=25+3=28`
and frequency of `70 = 7a-11=7(5)-11 (put a=5) `
`=35-11=24`
Hence, the frequencies of `30` and `70` are respectively, `28` and `24.`