JEE PYQ: Statistics Question 16
Question 16 - 2020 (06 Sep Shift 1)
If $\sum_{i=1}^{n}(x_i - a) = n$ and $\sum_{i=1}^{n}(x_i - a)^2 = na$, $(n, a > 1)$, then the standard deviation of $n$ observations $x_1, x_2, \ldots, x_n$ is:
(1) $a - 1$ (2) $n\sqrt{a-1}$ (3) $\sqrt{n(a-1)}$ (4) $\sqrt{a-1}$
Show Answer
Answer: (4) $\sqrt{a-1}$
Solution
S.D. $= \sqrt{a - 1}$.