Question

What is the standard deviation?

Answer 1

Standard deviation.

Variance is a measure of the dispersion of the data set from the mean The variance is written as ${\sigma }^2$and is given by

${\sigma }^2=\frac{1}{n}{\left(x_i-\overline{x}\right)}^2$

Where $x_1,x_2.....x_n$ are $n$ observations and$\overline{x}$ is the mean of the given observations

Standard Deviation:

The standard deviation is also a measure of the dispersion from the mean calculated as follows:

$$\begin{gathered} \mathrm{Standard}\mathrm{deviation}=\sqrt{\mathrm{variance}} \\ \Rightarrow \mathrm{Standard}\mathrm{deviation}=\sqrt{{\sigma }^2} \\ \Rightarrow \mathrm{Standard}\mathrm{deviation}=\sigma \end{gathered}$$

And given by

$\sigma =\sqrt{{\sigma }^2}=\sqrt{\frac{1}{n}{\left(x_i-\overline{x}\right)}^2}$

Hence, the standard deviation (or $\sigma$) is a measure of how widely distributed the data is in reference to the mean which is given by$\sigma =\sqrt{{\sigma }^2}=\sqrt{\frac{1}{n}{\left(x_i-\overline{x}\right)}^2}$.