Let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \ldots, n$ is $14$. Then $n$ is equal to ..... .

If $\sum_{i=1}^{10} (x_i - 15) = 12$ and $\sum_{i=1}^{10} (x_i - 15)^2 = 18$,find the standard deviation of the observations $x_1, x_2, \dots, x_{10}$.

From the data given below,state which group is more variable,$A$ or $B$?

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

The variance of the data $1, 2, 3, 5, 8, 13, 17$ is approximately

Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

If $A$ and $B$ are the variances of the first $n$ even numbers and the first $n$ odd numbers respectively,then: