📊 Variance Calculator
Calculate sample or population variance from a list of numbers and see the mean, squared deviations, and standard deviation.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Enter numbers separated by commas or spaces.
Please enter valid values.
Formula and Explanation
Calculate sample or population variance from a list of numbers and see the mean, squared deviations, and standard deviation.
| Concept | Formula or rule |
|---|---|
| Variance Calculator | Population: σ² = Σ(x − μ)² / N · Sample: s² = Σ(x − x̄)² / (n − 1) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For 4, 6, 8, 10 using sample variance, the mean is 7 and the squared deviations sum to 20.
✓ s² = 20 ÷ 3 = 6.667
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Using N instead of n − 1
Sample variance divides by n − 1 because the sample mean is estimated from the data.
Sample variance divides by n − 1 because the sample mean is estimated from the data.
⚠️
Mixing units
Variance is expressed in squared units, such as dollars² or cm².
Variance is expressed in squared units, such as dollars² or cm².
⚠️
Ignoring outliers
A single extreme value can increase variance substantially.
A single extreme value can increase variance substantially.
Practice Questions
1. Find the population variance of 2, 2, 4, 4.
Answer: 1
2. Find the sample variance of 1, 3, 5.
Answer: 4
3. What happens to variance if every value is multiplied by 3?
Answer: Variance is multiplied by 9.
Frequently Asked Questions
What is the difference between sample and population variance?▾
Population variance describes every member of a population. Sample variance estimates population variability from a sample and uses n − 1.
Can variance be negative?▾
No. Squared deviations are never negative, so variance is always zero or positive.
What does a variance of zero mean?▾
Every value in the dataset is identical.