Calculate variance

Calculate population or sample variance and standard deviation for a numeric list.

freeworks offlinenothing uploaded
ToolVariance Calculator
Input
Output
—
Put this on your own site

The frame below runs the same code as this page, in the reader's own browser. Nothing is sent to us, and nothing is sent to you.

Pick a dark background and the text and panels follow it, so the frame stays readable on a dark page.

Preview

How it works

The mean is subtracted from each observation, squared deviations are summed, and the total is divided by n for a population or n−1 for a sample. Standard deviation is the square root, returning spread to the original units.

  • Population variance is the initial description of the supplied list.
  • Sample variance needs at least two values.

Worked example

A population of eight numbers
The whole population, not a sample drawn from it
Input
											Values: [2,4,4,4,5,5,7,9]
Is sample: false
Output
												Count: 8
Mean: 5
Variance: 4
Standard deviation: 2

When to use this

Quality samples estimate process variability, statistics lessons compare denominators, and measurement reports pair variance with standard deviation.

Edge cases

  • One extreme observation has a squared effect and can dominate variance.
  • A single-value sample has no defined n−1 estimate and is rejected.
  • Variance is in squared units, so standard deviation is the comparable original-unit spread.

References