The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

$A$ data consists of $20$ observations $x_1, x_2, ..., x_{20}$. If $\sum_{i=1}^{20} (x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20} (x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:

In an experiment with $15$ observations of $x$,the results $\Sigma x^2 = 2830$ and $\Sigma x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

Find the standard deviation of the first $n$ natural numbers.

If the mean and standard deviation of $n$ observations $x_1, x_2, \dots, x_n$ are $\bar{x}$ and $\sigma$ respectively,then what is the sum of the squares of the observations?

If the variance of the terms in an increasing $A.P.$,$b_{1}, b_{2}, b_{3}, \ldots, b_{11}$ is $90$,then the common difference of this $A.P.$ is