1.

Average height & variance of `5` students in a class is `150` and `18` respectively. A new student whose height is `156 cm` is added to the group. Find new variance. (a) `20` (b) `22` (c) `16` (d) `14`A. 16B. 22C. 20D. 18

Answer» Correct Answer - C
Let `x_(1), x_(2), x_(3),x_(4),x_(5)` be the heights of five students. Then,
We have
` " Mean,"bar(x)=(sum_(i=1)^(5)x_(i))/(5)=150 rArr sum_(i=1)^(5)x_(i)=750 " ...(i) " `
` " and variance " =(sum_(i=1)^(5)x_(i)^(2))/(n)-(bar(x))^(2)`
`rArr (sum_(i=1)^(5)x_(i)^(2))/(5)-(150)^(2)=18`
`rArr sum_(i=1)^(5)x_(i)^(2)=112590 " ... (ii)" `
Now, new mean `=(sum_(i=1)^(6)x_(i))/(6)`
`=(sum_(i=1)^(5)x_(i)+156)/(6)=(750+156)/(6)` [using Eq. (i)]
`rArr bar(x)_("new") =151`
and new variance
`= (sum_(i=1)^(6)x_(i)^(2))/(6)-(bar(x)_("new"))^(2) =(sum_(i=1)^(5)x_(i)^(2)+(156)^(2))/(6)-(151)^(2)`
`=(112590+(156)^(2))/(6)-(151)^(2) " " ` [using Eq. (ii)]
`=22821 - 22801=20`


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