How to use the Standard Deviation Calculator
- 1. Paste your dataSeparate values with commas, spaces or new lines.
- 2. Press CalculateThe tool works out both types at once.
- 3. Read the workingSee the mean, variances and a table of squared gaps.
What standard deviation tells you
Standard deviation measures spread. A small value means your numbers sit close to the mean. A large value means they are scattered. Two classes can share the same average mark and still have very different spreads.
Sample or population?
Use population when your data covers the whole group, such as every student in one class. Divide the squared gaps by n.
Use sample when your data is a part of a bigger group, such as 50 students from a whole university. Divide by n − 1. This correction allows for the fact that a sample tends to understate the real spread.
The formulas are σ² = Σ(x − mean)² ÷ n and s² = Σ(x − mean)² ÷ (n − 1). Standard deviation is the square root of variance.
Worked example
Take 2, 4, 4, 4, 5, 5, 7 and 9.
- The sum is 40 and n is 8, so the mean is 5.
- The squared gaps from the mean are 9, 1, 1, 1, 0, 0, 4 and 16. They add up to 32.
- Population variance is 32 ÷ 8 = 4, so population SD is 2.
- Sample variance is 32 ÷ 7 = 4.571429, so sample SD is 2.13809.
With a single value, the sample version cannot be worked out, because n − 1 is 0. The tool tells you so.
Need just the mean and median? Use the average calculator. For other maths, try the scientific calculator.
Frequently asked questions
Should I use sample or population?
If your data is the whole group, use population. If it is part of a larger group, use sample.
Why is sample SD larger?
It divides by n − 1 rather than n, which gives a slightly larger value.
What happens with one number?
Population SD is 0. Sample SD needs at least two values, so the tool says so.
Is this tool free?
Yes. It asks for your name and WhatsApp number once, when your result is ready, and other Uncodemy tools then open without the form.