Variance Calculator
Calculate Population Variance, Sample Variance, and Standard Deviation.
Population Variance (σ²)
Use when data is the entire population
Sample Variance (s²)
Use when data is a sample of a larger population
Calculation Steps
| Data Point (x) | Difference (x - μ) | Square (x - μ)² |
|---|---|---|
| Sum (Σ) | 0 |
Step 1: Calculate the Mean (μ) = Sum of X / N = 0
Step 2: Subtract the mean from each data point and square the result (see table above).
Step 3: Sum the squared differences = 0
Step 4 (Population): Divide by N (0) = 0
Step 4 (Sample): Divide by N-1 (0) = 0
Sample and Population Variance, Explained
Paste your dataset and this free calculator instantly computes the mean, sample variance, population variance, and standard deviation — the core measures of how spread out your data is.
Choose the right formula for your situation: sample variance (n−1) when your data is a sample, population variance (n) when you have the whole population. Results appear instantly in your browser.
Sample vs population
Both formulas are computed side by side, with standard deviation and mean included, so you always pick the right one.
Instant results
Paste comma- or space-separated numbers and get the full statistical summary in one click.
Free and private
All statistics run locally in your browser — your dataset is never uploaded to a server.
How to use
- Paste your numbers separated by commas or spaces.
- Click Calculate.
- Read the mean, sample variance, population variance, and standard deviation.
Frequently Asked Questions
What is variance?
Variance measures how far numbers in a dataset spread out from the mean — higher variance means the values are more scattered.
What is the difference between sample and population variance?
Population variance divides by n (you have all the data); sample variance divides by n−1 to correct for estimating from a sample.
What is standard deviation?
The square root of variance — it expresses spread in the same units as your data, which is easier to interpret.
How should I enter my data?
Type or paste numbers separated by commas, spaces, or new lines.
Is my data uploaded anywhere?
No. All calculations happen in your browser — your dataset never leaves your device.
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