Variance Calculator
Compute sample or population variance, standard deviation and mean of any dataset. Paste comma-separated numbers for instant results.
Comma-separated numbers, e.g. 2, 4, 4, 4, 5, 5, 7, 9.
Variance
4.5714
Standard deviation
2.1381
Mean
5
8 values
Sample variance divides by n−1; population variance divides by n. Use sample for a survey, population for a full census.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Use the variance calculator whenever you need a precise measure of spread for a dataset — student marks, delivery times, monthly electricity bills, machine measurements or share price returns. Variance is the foundation of nearly every advanced statistic, from standard deviation and z-scores to analysis of variance and regression, so students and analysts across India use it to verify the first step of their calculations. Quality teams track variance to detect processes becoming less consistent, and finance students compare the variance of portfolio returns as a risk measure. The calculator produces mean, variance and standard deviation in one pass with a clear sample-versus-population choice, matching the convention used in textbooks and statistical software. Because it accepts comma-separated lists directly, checking a hand-computed result takes seconds rather than a spreadsheet session.
How to Use This Calculator
- Step 1: Paste or type your numbers in the values box, comma-separated.
- Step 2: Choose sample if the data is a random subset, population if it covers everything.
- Step 3: Check the mean, variance and standard deviation output together.
- Step 4: Compare with other datasets using the coefficient of variation when scales differ.
Worked Example
A teacher in Nagpur records eight students' marks — 2, 4, 4, 4, 5, 5, 7, 9 — as a sample of the class. Choosing sample mode gives a variance of 4.5714 and a standard deviation of 2.1381 around a mean of 5. If these eight marks were the entire class, the population variance would be 4 exactly with a standard deviation of 2 — the smaller divisor n instead of n−1 tightens the spread. For the simpler set 1, 2, 3, 4, 5 the sample variance is 2.5 with standard deviation 1.5811.
Tips and Common Mistakes
- •Tip 1: Use sample mode whenever your data is a subset estimating a larger group — the n−1 correction is required.
- •Tip 2: Report the standard deviation alongside the variance, since it is in the original units and easier to read.
- •Tip 3: Compare spread across differently scaled datasets with the coefficient of variation calculator instead.
- ✗Mistake 1: Mixing sample and population interpretations when quoting results — label which one you used.
- ✗Mistake 2: Using variance alone to compare datasets in different units — 4 kg² and 4 ₹² are not comparable.
Frequently Asked Questions
What is variance?
Variance measures how spread out a dataset is — the average of the squared distances from the mean. It squares the deviations so positive and negative differences do not cancel out. The square root of variance is the standard deviation, which is in the original units and easier to interpret.
What is the difference between sample and population variance?
Population variance divides by n and is used when your data covers every member of the group. Sample variance divides by n−1 and is used when the data is a random sample estimating a larger population — the n−1 correction makes the estimate unbiased. For the dataset 2, 4, 4, 4, 5, 5, 7, 9, the population variance is 4 but the sample variance is 4.571.
Why does variance square the deviations?
Squaring serves two purposes: it makes all terms positive so they cannot cancel, and it penalizes large deviations disproportionately. A value three units away contributes nine times as much as a value one unit away. The downside is that units get squared (₹², kg²), which is why the standard deviation — the square root — is reported for everyday use.
How do I use this for marks or prices in India?
Paste comma-separated values like student marks, share prices or monthly electricity bills. If you have every observation — all students in one class, say — choose population. If you are estimating from a sample, like a price survey, choose sample. The output gives variance, standard deviation and mean together.
What is a good or bad variance value?
It depends entirely on the scale of the data — a variance of 4 is small for income in lakhs but large for temperatures in degrees. That is why relative measures like the coefficient of variation calculator are better for comparing spread across different datasets, while variance and standard deviation describe spread in absolute terms.
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