If both mean and variance of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$ and $256$ respectively,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

Based on the following statements,choose the correct option.
Statement-$I:$ The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.
Statement-$II:$ The difference between the variance of the first $20$ even natural numbers and their arithmetic mean is $112$.

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

If the mean of the distribution is $2.6$,then the value of $y$ is:

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

If both mean and variance of $50$ observations $x_1, x_2, \ldots, x_{50}$ are equal to $16$ and $256$ respectively,then the mean of $(x_1-5)^2, (x_2-5)^2, \ldots, (x_{50}-5)^2$ is

The mean of a series $x_1, x_2, \dots, x_n$ is $\bar{X}$. If $x_2$ is replaced by $\lambda$,what will be the new mean?