Naima Cox

2022-01-28

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

tsjutten20

Beginner2022-01-29Added 13 answers

Population standard deviation:

$\sigma =\sqrt{\frac{{({x}_{1}-\stackrel{\u2015}{x})}^{2}+{({x}_{2}-\stackrel{\u2015}{x})}^{2}+(\dots )+{({x}_{n}-\stackrel{\u2015}{x})}^{2}}{n}}$

Sample standard deviation:

$s=\sqrt{\frac{{({x}_{1}-\stackrel{\u2015}{x})}^{2}+{({x}_{2}-\stackrel{\u2015}{x})}^{2}+(\dots )+{({x}_{n}-\stackrel{\u2015}{x})}^{2}}{n-1}}$

The procedure for calculating a sample's standard deviation is as follows:

Find the mean of the set of numbers: $\stackrel{\u2015}{x}=\frac{{x}_{1}+{x}_{2}+\dots +{x}_{n}}{n}$ where n = the number of numbers in the set.

Subtract the mean from each number in your sample, square the difference and add: $({x}_{1}-\stackrel{\u2015}{x})}^{2}+{({x}_{2}-\stackrel{\u2015}{x})}^{2}+(\dots )+{({x}_{n}-\stackrel{\u2015}{x})}^{2$

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:

$s=\sqrt{\frac{{({x}_{1}-\stackrel{\u2015}{x})}^{2}+{({x}_{2}-\stackrel{\u2015}{x})}^{2}+(\dots )+{({x}_{n}-\stackrel{\u2015}{x})}^{2}}{n-1}}$

egowaffle26ic

Beginner2022-01-30Added 7 answers

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.