The standard deviation of $25$ numbers is $40$. If each of the numbers is increased by $5$, then the new standard deviation will be

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to

Determine mean and standard deviation of first n terms of an $A.P.$ whose first term is a and common difference is d.

For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true

In a series of $2n$ observation, half of them are equal to $'a'$  and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals

The $S.D$ of $15$ items is $6$ and if each item is decreased or increased by $1$, then standard deviation will be