Variance and Standard Deviation

Standard Deviation calculation involves many mathematical processes.

Calculate the variance and standard deviation for the following data:

$5, 7, 8, 11, 12, 5, 10, 14$

Standard Deviation calculation is based on all the observations of a series.

Calculate the variance and standard deviation for the following data:

$6, 7, 8, 11, 13, 4, 10, 13$

For the data given, find standard deviation.

Find standard deviation for the given data $\Sigma f_i{x}_i=10, \Sigma f_i{x_i}^2=50, \Sigma f_i=10$.

For the data given, find variance.

Find variance for the given data $\Sigma f_i{x}_i=10, \Sigma f_i{x_i}^2=50, \Sigma f_i=10$.

The snow recorded in various places of five districts in a week are given below. 

$\begin{array}{|ccccccc|}\hline \mathrm{snow}& \mathbf{45}& \mathbf{50}& \mathbf{55}& \mathbf{60}& \mathbf{65}& \mathbf{70}\\ \begin{array}{c}\mathrm{Number}of\\ \mathrm{places}\end{array}& \mathbf{5}& \mathbf{13}& \mathbf{4}& \mathbf{9}& \mathbf{5}& \mathbf{4}\\ \hline\end{array}$

Find its variance.

The snow recorded in various places of five districts in a week are given below. 

$\begin{array}{|ccccccc|}\hline \mathrm{snow}& \mathbf{45}& \mathbf{50}& \mathbf{55}& \mathbf{60}& \mathbf{65}& \mathbf{70}\\ \begin{array}{c}\mathrm{Number}of\\ \mathrm{places}\end{array}& \mathbf{5}& \mathbf{13}& \mathbf{4}& \mathbf{9}& \mathbf{5}& \mathbf{4}\\ \hline\end{array}$

Find its standard deviation.

If the standard deviation of a data is $5$ and each value of the data is multiplied by $-4$, then find the new standard deviation.

If the standard deviation of a data is $5$ and each value of the data is multiplied by $3$, then find the new standard deviation.

If the variance of a data is $5$ and each value of the data is multiplied by $3$, then find the new variance.

If the variance of a data is $3$ and each value of the data is multiplied by $2$, then find the new variance.

If the standard deviation of a data is $6$ and each value of the data is increased by $3$, then find the new standard deviation.

If the variance of a data is $3$ and each value of the data is increased by $2$, then find the new variance.

If the variance of a data is $4$ and each value of the data is increased by $2$, then find the new variance.

If the standard deviation of a data is $4$ and each value of the data is increased by $2$, then find the new standard deviation.

Find the variance, when standard deviation of the data is $11$.

Find the variance, when standard deviation of the data is $5$.