Variance Calculator

Solve s² = Σ(x − x̄)² / (n − 1) step by step — free variance calculator with worked examples, real-world defaults and instant answers.

s² = Σ(x − x̄)² / (n − 1)

Data set7 values

Sample variance s²5.80952

Population variance σ²4.97959

Mean14.1429

SD (sample)2.4103

1
Mean first:
x̄ = 99/7 = 14.1429
2
Sum of squared deviations:
SS = Σ(x − x̄)² = 34.8571
3
Divide by n − 1 for the sample variance:
s² = 34.8571 / 6 = 5.80952
4
Variance is in SQUARED units — its square root (the SD) restores the original units:
s = √5.80952 = 2.4103

Variance is the average squared distance from the mean. It's the quantity that adds nicely (variances of independent variables sum — the basis of error propagation and portfolio risk), while the SD is the one you can interpret in original units.

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Variance — the squared-units measure of spread, sample and population.

About Variance Calculator

The Variance Calculator solves s² = Σ(x − x̄)² / (n − 1) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. Variance is the average squared distance from the mean.

How to use Variance Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into s² = Σ(x − x̄)² / (n − 1) and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Variance Calculator?

✓Solves s² = Σ(x − x̄)² / (n − 1) instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Variance Calculator use?+

It uses s² = Σ(x − x̄)² / (n − 1). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Variance Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Variance Calculator on your website

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