Statistics
Variance Calculator
Focus solely on variance with a clean interface for sample or population datasets.
Enter values, pick sample or population, and get variance with the matching standard deviation.
Variance definition
Variance = Σ(x − mean)² / (n − δ)
δ equals 1 for sample variance (n − 1 divisor) and 0 for population variance (n divisor).
How to use
- Paste or type values separated by commas or spaces.
- Pick sample or population mode depending on your dataset.
- Review variance and standard deviation results with the same units squared.
Example
Input: Values = 4, 9, 11, 15
Output: Sample variance ≈ 20.92, Sample σ ≈ 4.57
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Variance Calculator: statistics calculator, variance calculator, standard deviation calculator, probability calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Variance Calculator: Calculates data variability around the mean as variance and standard deviation. It's built around variance, spread, standard deviation, so you can go from a raw question to a checked answer without switching tools.
The math behind it: δ equals 1 for sample variance (n − 1 divisor) and 0 for population variance (n divisor). The core relationship is Variance = Σ(x − mean)² / (n − δ), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Paste or type values separated by commas or spaces. (2) Pick sample or population mode depending on your dataset. (3) Review variance and standard deviation results with the same units squared. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Values = 4, 9, 11, 15 returns Sample variance ≈ 20.92, Sample σ ≈ 4.57. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Why is variance shown in squared units?
Variance squares the distance from the mean, so the unit is squared. The calculator also shows standard deviation to bring it back to the original scale.
Can I export the results?
Copy the displayed values directly—everything is formatted for quick pasting into reports or spreadsheets.
What formula does the Variance Calculator use?
δ equals 1 for sample variance (n − 1 divisor) and 0 for population variance (n divisor).
How do I use the Variance Calculator?
Paste or type values separated by commas or spaces. Pick sample or population mode depending on your dataset. Review variance and standard deviation results with the same units squared.