Standard deviation, step by step.
The steps of a standard deviation on your own numbers, and when to divide by n − 1 for a sample or by n for a whole population.
By Suraj Kumar2 min read
Standard deviation says how far numbers typically sit from their mean.
The steps.
Find the mean; take it from each number and square; add the squares; divide by n − 1 for a sample or n for a population; take the square root. For 2, 4, 4, 4, 5, 5, 7, 9: mean 5, squares 32, sample variance 32 ÷ 7, standard deviation about 2.1381.
Why n − 1.
A sample's own mean sits closer to its numbers than the whole group's would, so dividing by n − 1 (Bessel's correction) makes up for it.
Your working.
Open The working under the answer to see each step on your numbers.
Further reading
Topics: standard deviation calculator · how to calculate standard deviation · sample standard deviation · population standard deviation · sd formula
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