Population vs Sample Variance Calculator
Compare population and sample variance/standard deviation for a dataset.
Enter your values
Enter the dataset (comma-separated) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Mean
- 5.5
- Population variance
- 2.9167
- Sample variance
- 3.5
- Population std dev
- 1.7078
- Sample std dev
- 1.8708
Quick answer
Population variance divides squared deviations by n; sample variance divides by n-1 (Bessel's correction) to correct for bias when estimating from a sample.
σ² = Σ(x-μ)²/n, s² = Σ(x-x̄)²/(n-1)
At a glance
| What it does | Compare population and sample variance/standard deviation for a dataset. |
|---|---|
| Category | Statistics |
| Inputs needed | Dataset (comma-separated) |
| Main output | Mean |
| Formula | σ² = Σ(x-μ)²/n, s² = Σ(x-x̄)²/(n-1) |
| Cost | Free — no sign-up, no download |
How to use the Population vs Sample Variance Calculator
- 1Enter your full dataset as comma-separated numbers.
- 2Population variance divides by n, treating the data as the entire population.
- 3Sample variance divides by n-1 instead, correcting for bias when the data is only a sample.
Inputs explained
- Dataset (comma-separated)
- Enter the dataset (comma-separated) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Dataset (comma-separated)4,8,6,5,3,7
Results
- Mean5.5
- Population variance2.9167
- Sample variance3.5
- Population std dev1.7078
- Sample std dev1.8708
Frequently asked questions
Which one should I use?
Use sample variance whenever your data is a sample used to estimate a larger population; use population variance only if you truly have the whole population.
Why is sample variance always larger?
Dividing by the smaller n-1 instead of n inflates the estimate slightly to correct for using the sample mean instead of the true mean.
What do I need to enter into the Population vs Sample Variance Calculator?
Just 1 value: dataset (comma-separated). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Population vs Sample Variance Calculator work out the answer?
Population variance divides squared deviations by n; sample variance divides by n-1 (Bessel's correction) to correct for bias when estimating from a sample. It applies the formula σ² = Σ(x-μ)²/n, s² = Σ(x-x̄)²/(n-1) and shows the working so you can check each step by hand.
Is the Population vs Sample Variance Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.