Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is
$4$
$6$
$8$
$2$
Let $X=\{11,12,13, \ldots ., 40,41\}$ and $Y=\{61,62$, $63, \ldots ., 90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$, then $\left|\overline{ x }+\overline{ y }-\sigma^2\right|$ 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.