If $M.D.$ is $12$,the value of $S.D.$ will be

In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a+k, b+k, c+k, d+k$ and $e+k$ is

Let $x_1, x_2, \dots, x_n$ be $n$ observations,$\bar{x}$ be their mean,and $\sigma^2$ be their variance.
Statement-$1$: The variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$.
Statement-$2$: The mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.

Find the variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$

Suppose values taken by a variable $x$ are such that $a \le x_i \le b$,where $x_i$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ..., n$. Then: