Standard Deviation Calculator
The Standard Deviation Calculator shows how far your numbers spread from their mean, for either a full population or a sample. It also reports the mean, count and variance, so you can describe any dataset at a glance.
What this means
Standard deviation tells you how consistent your data is. A low value means the numbers hug the average; a high value means they spread widely. In finance, it is the classic measure of risk and volatility.
How we calculate it
Formula
σ = √(Σ(xᵢ − mean)² ÷ n) for a population, or ÷ (n − 1) for a sample.Worked example
Numbers 2, 4, 4, 4, 5, 5, 7, 9:
- 1Mean = 5
- 2Population variance = 4
- 3Standard deviation = √4 = 2
Important assumptions
- The sample formula divides by n − 1; the population formula divides by n.
Frequently asked questions
Population vs sample: which should I use?
Use population when your list includes every member of the group. Use sample when it is a subset used to estimate the whole group.
What does a high standard deviation mean?
The values vary widely from the average — more risk, more volatility, more spread.
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