Standard Deviation Calculator

The standard deviation measures how spread out the data is from the mean. The smaller it is, the more tightly the data clusters around the mean; the larger it is, the more widely spread the data.

Enter comma-separated numbers to calculate both the mean and the population standard deviation. Used to assess data variability in grade distributions or quality control.

For example, the mean of 10, 20, 30, 40, 50 is 30, and the standard deviation is about 14.14.

Standard Deviation Calculator Calculation Method

Number list (comma-separated)

Average: 0

Standard deviation: 0

About This Calculator

Standard deviation measures how spread out a set of values is around its mean. A small value means the data clusters tightly; a large one means it is widely scattered. It is the basis of volatility, quality control and test-score analysis.

Enter comma-separated numbers to get the mean and the population standard deviation.

Standard deviation is the square root of the average squared distance from the mean, so it carries the same units as the data. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2. In a normal distribution about 68 % of values fall within one standard deviation and 95 % within two.

Key Formula:σ = √( Σ(xᵢ − μ)² / N )

Frequently Asked Questions

What is the difference between population and sample standard deviation?

Population standard deviation divides by N, the full count; sample standard deviation divides by N − 1 to correct for the fact that a sample mean is only an estimate. The sample version is always slightly larger.

What does one standard deviation cover?

In a normal distribution about 68% of values fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three — the empirical rule.

What does standard deviation mean in finance?

It measures volatility, the spread of returns around their average. Two funds returning 7 % with standard deviations of 10 % and 20 % carry very different risk, which is why the Sharpe ratio divides excess return by volatility.

What does a standard deviation of zero mean?

Every value is identical, so the mean is the only possible observation. Any spread at all, however small, produces a value above zero, which makes it useful for spotting constant or frozen sensor readings.

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Sources & last update

2026-10-19