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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 |
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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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