What's the difference between population and sample standard deviation?

Population standard deviation is used when the data represents an entire population; sample standard deviation divides by (n-1) instead of n to correct for underestimating variability when the data is only a sample of a larger population.

Can two data sets have the same average but different standard deviations?

Yes, and it happens often. The average describes the center of the data, while standard deviation describes how spread out the values are around that center — the two measure different things.

What is variance compared to standard deviation?

Variance is the average of the squared differences from the mean. Standard deviation is the square root of variance, which brings the measure back into the same units as the original data.

Standard Deviation Calculator

Paste or type your data and get full descriptive statistics instantly — mean, median, mode, variance, standard deviation, quartiles, and more.

Data values (comma or newline separated)

How to use

Enter your numbers in the text area, separated by commas or on separate lines.
Click Calculate to compute all statistics at once.
Population standard deviation (σ) divides by n — use when your data is the entire population.
Sample standard deviation (s) divides by n−1 — use when your data is a sample from a larger group.
The sorted data view highlights Q1 (green), the median (teal), and Q3 (yellow) for quick reference.
Use Copy Results to copy all statistics to your clipboard.

About this Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is from the average. A low standard deviation means values cluster tightly around the mean; a high standard deviation means values are widely scattered, even if the average is the same in both cases.

Why average alone can be misleading

Two data sets can have the identical average but look completely different: {50, 50, 50, 50} and {10, 30, 70, 90} both average to 50, but the first set has zero variation while the second is widely spread. Standard deviation captures that difference, which the average alone cannot show.

Population vs. sample standard deviation

If your data represents an entire population (every value that exists), use population standard deviation. If your data is a sample drawn from a larger population (common in surveys, experiments, and most real-world statistics), use sample standard deviation, which divides by (n−1) instead of n to correct for the tendency of a sample to underestimate true variability. Most statistical work uses the sample formula unless the full population is genuinely known.

The calculation steps

Find the mean (average) of the data set
Subtract the mean from each value and square the result
Average those squared differences (this is the variance)
Take the square root of the variance to get the standard deviation