Naima Cox

2022-01-28

How do you find the standard deviation of a set of numbers?

tsjutten20

Population standard deviation:
$\sigma =\sqrt{\frac{{\left({x}_{1}-\stackrel{―}{x}\right)}^{2}+{\left({x}_{2}-\stackrel{―}{x}\right)}^{2}+\left(\dots \right)+{\left({x}_{n}-\stackrel{―}{x}\right)}^{2}}{n}}$
Sample standard deviation:
$s=\sqrt{\frac{{\left({x}_{1}-\stackrel{―}{x}\right)}^{2}+{\left({x}_{2}-\stackrel{―}{x}\right)}^{2}+\left(\dots \right)+{\left({x}_{n}-\stackrel{―}{x}\right)}^{2}}{n-1}}$

The procedure for calculating a sample's standard deviation is as follows:
Find the mean of the set of numbers: $\stackrel{―}{x}=\frac{{x}_{1}+{x}_{2}+\dots +{x}_{n}}{n}$ where n = the number of numbers in the set.
Subtract the mean from each number in your sample, square the difference and add: ${\left({x}_{1}-\stackrel{―}{x}\right)}^{2}+{\left({x}_{2}-\stackrel{―}{x}\right)}^{2}+\left(\dots \right)+{\left({x}_{n}-\stackrel{―}{x}\right)}^{2}$
To determine the variance of your collection, divide these numbers by n-1.

An impartial sample variance is produced by dividing by n-1.

To find the standard deviation from the mean, square root the variance:
$s=\sqrt{\frac{{\left({x}_{1}-\stackrel{―}{x}\right)}^{2}+{\left({x}_{2}-\stackrel{―}{x}\right)}^{2}+\left(\dots \right)+{\left({x}_{n}-\stackrel{―}{x}\right)}^{2}}{n-1}}$

egowaffle26ic

Calculate the Mean (the arithmetic average of the numbers); after that, for each value, take the Mean out and square the result.

Calculate the mean of those squared differences next.

We are done after taking that's square root.

Do you have a similar question?