JEE PYQ: Statistics Question 31
Question 31 - 2019 (09 Jan Shift 2)
A data consists of $n$ observations: $x_1, x_2, \ldots, x_n$. If $\sum_{i=1}^{n}(x_i + 1)^2 = 9n$ and $\sum_{i=1}^{n}(x_i - 1)^2 = 5n$, then the standard deviation of this data is:
(1) 2 (2) $\sqrt{5}$ (3) 5 (4) $\sqrt{7}$
Show Answer
Answer: (2) $\sqrt{5}$
Solution
$A = 6n$, $B = n$. $\sigma^2 = 6 - 1 = 5$. $\sigma = \sqrt{5}$.