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If the standard deviation of the numbers...

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ? (1) `3a^2-26 a+55=0` (2) `3a^2-32 a+84=0` (3) `3a^2-34 a+91=0` (4) `3a^2-23 a+44=0`

A

`3a^(2)-32a+84=0`

B

`3a^(2)-34a+91=0`

C

`3a^(2)-23a+44=0`

D

`3a^(2)-26a+55=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Standard deviation of numbers 2,3,a and 11 is 3.5
`therefore (3.5)^(2)=(sum x_(i)^(2))/(4)-(overline(x))^(2)`
`implies (3.4)^(2)=(4+9+a^(2)+121)/(4)-((2+3+a+11)/(4))^(2)`
On solving, we get
`3a^(2)-32a+84=0`
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