Numarly

Variance Calculator

Calculate variance of a dataset easily

What is it?

Variance measures how far each number in a dataset is from the mean, on average, using squared differences. It's the foundation for standard deviation and many statistical tests.

Formula

Variance = Σ(x − mean)² / n

Formula Explanation

Squaring each value's distance from the mean before averaging ensures differences on either side of the mean don't cancel each other out, and gives proportionally more weight to values that are further from the mean.

Example Calculation

For 10, 20, 30: mean = 20, squared differences = 100, 0, 100, so variance = (100+0+100)/3 ≈ 66.67.

How to Use

  1. Enter your numbers separated by commas (e.g. 10, 20, 30).
  2. Click Calculate Variance.
  3. View the mean, variance, and a bar chart of your data.

Benefits

  • Computes mean and variance together in a single step.
  • Shows the full step-by-step calculation for learning purposes.
  • Visualizes your data against the mean with a bar chart.

Use Cases

  • Foundational calculation for standard deviation, correlation, and regression analysis.
  • Quantifying risk or volatility in financial data.
  • Quality control processes measuring consistency of measurements.

What Your Result Means

A larger variance means your data points are, on average, further from the mean — more spread out. A smaller variance means the data clusters more tightly around the mean. Variance is expressed in squared units of your data.

Tips

  • Take the square root of variance to get the standard deviation, which is easier to interpret in original units.
  • Compare variances only when datasets use the same units.
  • A variance of 0 means every value in the dataset is identical.

Common Mistakes

  • Forgetting to square the deviations before averaging.
  • Interpreting variance directly in the data's original units — it's actually in squared units.
  • Using population variance formula (÷n) when a sample-based formula (÷(n−1)) is statistically required.

FAQs

Why are the differences squared?

Squaring prevents positive and negative differences from canceling out and gives larger deviations proportionally more weight.

How is variance different from standard deviation?

Standard deviation is the square root of variance — variance is in squared units, while standard deviation returns to the original units, making it more intuitive to interpret.

Example calculation?

For data 10, 20, 30: mean = 20, differences = -10, 0, 10, squared = 100, 0, 100, variance = (100+0+100)/3 = 66.67.

What does a variance of 0 mean?

A variance of 0 means every value in the dataset is exactly the same, with no spread at all.

Is this population or sample variance?

This calculator computes population variance (dividing by n). Sample variance, used for estimating a larger population from a sample, divides by n−1 instead.

This calculator computes population variance (dividing by n, not n−1).

Last updated: July 25, 2026