If the mean of the following data is 20.2, then find the value of p.

Explanation

We know that,
Mean of the data `(barx)= (underset(i=1)overset(5)Sigmaf_(i)x_(i))/(underset(i=1)overset(5)Sigmaf_(i)=20.2` (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))=20.2`
`rArr ((6)(10)+(8)(15)+(p)(2)+(1)(25)+(6)(30))/(30+p)=20.2`
`rArr (60+120+20p+250+180)/(30+p)=20.2`
`rArr 20p+610=606+20.2p`
`rArr 610-606=0.2p`
`rArr (2p)/(10)=4`
`therefore p=10 xx 2=20`
Hence, the value of p is 20.