Statistics & Probability

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Population Variance Calculator.

Calculate population variance and population standard deviation for an entered finite data set.

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01

Set your values

Results update as you type.

populationVariance: 6.16

populationVariance

6.160000
populationStandardDeviation: 2.481935

populationStandardDeviation

2.481935
mean: 5.2

mean

5.200000
count: 5

count

5.000000

This route intentionally uses denominator N (population variance), not the sample denominator N − 1.

Results update automatically as you type.

Use Cases

Quality control in manufacturing

Assess the consistency of product measurements (e.g., dimensions, weights) across an entire production batch to ensure they meet specifications.

Example: Enter the weights of all 1000 items produced in a day to see how much they vary.

Academic research with complete datasets

Analyze the spread of scores or measurements when you have data from every subject in your study, such as all students in a class.

Example: Enter the test scores of all 30 students in a class to find the variance.

Frequently Asked Questions

What is population variance?
Population variance measures how spread out the numbers in a complete data set are from the mean. It is calculated by averaging the squared differences from the mean. This calculator provides both the variance and the standard deviation (the square root of variance).
How do I use this calculator?
Enter your data values separated by commas or spaces in the 'Data values' field. The calculator will compute the population variance and standard deviation. Ensure you include all values from your entire population, not a sample.
What is the difference between population and sample variance?
Population variance uses the entire data set (N) and divides by N. Sample variance uses a subset and divides by N-1. This calculator is specifically for population variance, so use it when your data represents the whole group you're studying.

Tips & Common Mistakes

Tips

  • Separate each data value with a comma or space. For example: 10, 12, 15, 18.
  • Double-check that you have included every value from your population; missing data will skew the variance.
  • Use the standard deviation result for a more intuitive measure of spread, as it is in the same units as your data.
  • If you have a sample (not the entire population), use a sample variance calculator instead.

Common Mistakes to Avoid

  • Using sample data when you intend to calculate population variance. This calculator assumes your data is the entire population.
  • Forgetting to include all data points or accidentally duplicating entries, which can distort the variance.
  • Confusing variance with standard deviation. Variance is the squared deviation, while standard deviation is its square root.

Last updated: August 13, 2026