The mean of $5$ observations is $15$ and variance is $9$. If two observations having values $-5$ and $13$ are combined with these observations,then what will be the new variance?

If the variance of $10$ natural numbers $1, 1, 1, \dots, 1, k$ is less than $10$,then the maximum possible value of $k$ is ...... .

If $X$ is a random variable such that $\sigma(X) = 2.6$, then $\sigma(1 - 4X)$ is equal to:

For $10$ observations $x_1, x_2, ..., x_{10}$, if $\sum_{i=1}^{10} (x_i + 2)^2 = 180$ and $\sum_{i=1}^{10} (x_i - 1)^2 = 90$, then their standard deviation is:

For a data consisting of $15$ observations $x_i$,$i=1, 2, 3, \ldots, 15$,the following results are obtained: $\sum_{i=1}^{15} x_i = 170$ and $\sum_{i=1}^{15} x_i^2 = 2830$. If one of the observations,namely $20$,was found to be wrong and was replaced by its correct value $30$,then the corrected variance is:

Calculate the variance of the following continuous frequency distribution:

Class Interval	$0$–$4$	$4$–$8$	$8$–$12$	$12$–$16$
Frequency $(f_i)$	$1$	$2$	$2$	$1$