If the standard deviation of the numbers 2, 3, a and 11 is 3, 5, then which of the following is true ?

Options

A. `3a^(2)-26a+55=0`
B. `3a^(2)-32a+84=0`
C. `3a^(2)-34a+91=0`
D. `3a^(2)-23a+44=0`

Answer

B

Explanation

We know that, if `x_(1), x_(2), … x_(n)` are n observations, then their standard deviation is given by `sqrt((1)/(n)Sigmax_(i)^(2)-((Sigma_(i))/(n))^(2))`
We have, `(3.5)^(2)=(2^(2)+3^(2)+a^(2)+11^(2))/(4)-((2+3+a+11)/(4))^(2)`
`rArr (49)/(4)=(4+9+a^(2)+121)/(4)-((16+a)/(4))^(2)`
`rArr (49)/(4)=(134+a^(2))/(4)-(256+a^(2)+32a)/(16)`
`rArr (49)/(4) = (4a^(2)+536-256-a^(2)-32a)/(16)`
`rArr 49 xx 4= 3a^(2) -32a +280 rArr 3a^(2)-32a+84 =0`