Guide

Sample vs population standard deviation

Use σ when the list is the entire population. Use s when the list is a sample you will use to infer a larger group. Both start the same way: mean, then squared deviations, then a square root. Only the divisor changes.

Why n − 1 exists

A sample usually sits closer to its own mean than to the mean of the whole population, so dividing by n makes the spread look smaller than it really is. Dividing by n − 1 (Bessel’s correction) corrects that bias. When your values are the entire population there is nothing to correct, so you divide by N.

Same numbers, two questions

The worked set 10, 34, 23, 54, 9 shows both results side by side in the app. s is a little larger than σ because the divisor is 4 instead of 5.

Sample if these five are a draw from a larger group (divide by n − 1 = 4).
Population if they are the whole group (divide by N = 5).

Tips

Read the exam or lab prompt first. “These 30 students in the class” is often population. “A sample of 30 from the school” is sample.
Graphing calculators label Sx as sample and σx as population. This app uses the words Sample and Population on a switch.

Common mistakes

Always using n − 1 “because that is what the calculator default is.”
Mixing s in a formula that expects σ, or the reverse.

How Standard Deviation Calculator helps

Switch Sample and Population on the same pasted list. The headline symbol changes between s and σ, and Show solution changes the divisor line. You do not re-enter the numbers.

Switch sample and population on Android

Sample or population toggle on the Standard Deviation Calculator home screen