Find the variance of the following data:

Size $(x_i)$	$3.5$	$4.5$	$5.5$	$6.5$	$7.5$	$8.5$	$9.5$
Frequency $(f_i)$	$3$	$7$	$22$	$60$	$85$	$32$	$8$

Find the variance of the first $n$ natural numbers.

Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

The arithmetic mean and standard deviation of a data set of nine numbers are $13$ and $5$ respectively. If $3$ is included as the $10^{th}$ item of the data,then the variance of the data set of ten numbers is:

If the sum of $10$ observations and the sum of their squares are $12$ and $18$ respectively,then the standard deviation of the observations is:

Let $X_{1}, X_{2}, \ldots, X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}(X_{i}-\alpha)=36$ and $\sum_{i=1}^{18}(X_{i}-\beta)^{2}=90$,where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1$,then the value of $|\alpha-\beta|$ is ...... .