If $\sum_{i=1}^{10} (x_i - 15) = 12$ and $\sum_{i=1}^{10} (x_i - 15)^2 = 18$,find the standard deviation of the observations $x_1, x_2, \dots, x_{10}$.

In a data set with $15$ observations $x_1, x_2, x_3, \ldots, x_{15}$,we are given $\sum_{i=1}^{15} x_i^2 = 3600$ and $\sum_{i=1}^{15} x_i = 175$. If the value of one observation $20$ was found to be incorrect and was replaced by its correct value $40$,then the corrected variance of the data is:

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

The variance of the ungrouped data $2, 12, 3, 11, 5, 10, 6, 7$ is

If for a distribution,$\Sigma(x-5)=3$ and $\Sigma(x-5)^2=43$ and the total number of observations is $18$,then the variance of the distribution is

The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is