256 Tools

Standard Deviation Calculator

Std dev (population, σ)2
Std dev (sample, s)2.13809
Mean5
Count (n)8
Variance (population)4
Variance (sample)4.571429
Sum40
Range7
Min2
Max9

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Paste a list of numbers — separated by commas, spaces, or new lines — and this calculator returns the mean, variance, and standard deviation for both a whole population and a sample, along with the sum, count, min, max, and range. Everything is computed in your browser.

How to use

  1. Paste your numbers, separated by commas, spaces, or lines.
  2. Read the mean and standard deviation below.
  3. Use the population value for a full dataset, or the sample value for a sample.

How it works

First the mean (average) is found by dividing the sum by the count. Then each number's difference from the mean is squared and these are added up. Dividing that total by n gives the population variance; dividing by n−1 gives the sample variance, which corrects for estimating from a sample. The standard deviation is the square root of the variance.

Standard deviation equals the square root of the average squared distance from the mean.σ = √( Σ(x − μ)² / N )

Features

Population & sample

Get both σ (population) and s (sample) at once.

Full summary

Also shows sum, count, mean, min, max, and range.

Flexible input

Accepts commas, spaces, new lines, decimals and negatives.

Private & instant

All math runs in your browser; nothing is uploaded.

When to use it

Statistics homework

Check the spread of a dataset and your working.

Lab & science

Summarize the variability of measurements.

Grades & scores

See how consistent a set of results is.

Quick analysis

Get the spread of any pasted numbers fast.

Notes

  • Use population (σ) for a complete dataset.
  • Use sample (s) when the numbers are a sample of a larger group.
  • Sample values need at least two numbers.
  • All calculations run on your device; nothing is uploaded.

FAQ

What's the difference between population and sample?
Population divides by n; sample divides by n−1 to correct for estimating from a sample. Use sample when your data is a subset of a larger group.
What input does it accept?
Numbers separated by commas, spaces, or new lines, including decimals and negatives.
Why is the sample value blank?
Sample variance and standard deviation need at least two numbers, since they divide by n−1.
What is variance?
The average of the squared differences from the mean. Standard deviation is its square root, in the original units.
Is my data uploaded?
No. Everything is calculated in your browser and nothing leaves your device.

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