Statistics: If sum_i=1^16(a_i-6)=8 and sum_i=1^16(a_i-6)^2=40 , then the… | JEE Main 2021 | Yukti Vault

Yukti Vault

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 1

If $\sum_{i=1}^{16}(a_i-6)=8$ and $\sum_{i=1}^{16}(a_i-6)^{2}=40$, then the standard deviation of $a_1,a_2,\ldots,a_{16}$ is

Statistics

$\frac{2}{3}$$\frac{3}{2}$✓ Correct answer$\frac{5}{2}$$\frac{2}{5}$

Solution

Let $d_i=a_i-6$. SD is shift invariant. Variance $=\frac{40}{16}-\left(\frac{8}{16}\right)^2=\frac52-\frac14=\frac94$. SD $=\frac32$. Option B.

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