The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

The variance of the following continuous frequency distribution is
$\begin{array}{|l|c|c|c|c|}\hline \text{Class interval} & 0-4 & 4-8 & 8-12 & 12-16 \\ \hline \text{Frequency} & 2 & 3 & 2 & 1 \\ \hline\end{array}$

Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b$,where $a > b$,be $5$ and $10$ respectively. Then the Variance of the observations $n+x_n$ for $n=1, 2, 3, 4, 5$ is:

Find the mean and variance for the first $n$ natural numbers.

The standard deviation of the following distribution is:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$1$	$3$	$4$	$2$

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: