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

Population standard deviation: 
${\displaystyle \sigma =\sqrt{\frac{{(x_1-\bar{x})}^2+{(x_2-\bar{x})}^2+(\dots )+{(x_n-\bar{x})}^2}{n}}}$ 
Sample standard deviation: 
${\displaystyle s=\sqrt{\frac{{(x_1-\bar{x})}^2+{(x_2-\bar{x})}^2+(\dots )+{(x_n-\bar{x})}^2}{n-1}}}$ 

The procedure for calculating a sample's standard deviation is as follows:
Find the mean of the set of numbers: ${\displaystyle \bar{x}=\frac{x_1+x_2+\dots +x_n}{n}}$ where n = the number of numbers in the set. 
Subtract the mean from each number in your sample, square the difference and add: ${\displaystyle {(x_1-\bar{x})}^2+{(x_2-\bar{x})}^2+(\dots )+{(x_n-\bar{x})}^2}$ 
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: 
${\displaystyle s=\sqrt{\frac{{(x_1-\bar{x})}^2+{(x_2-\bar{x})}^2+(\dots )+{(x_n-\bar{x})}^2}{n-1}}}$

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.