Variance Calculator
Find the statistical variance of numerical data. Get instant step-by-step solutions — completely free, no signup required.
Free Variance Calculator Calculator
Enter your problem below to get an instant step-by-step solution.
About Variance Calculator
Find the statistical variance of numerical data. Statistics is the science of collecting, analyzing, and interpreting numerical data. Statistical methods are used in research, business, medicine, and machine learning.
Our Variance Calculator calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any variance calculator expression and receive a complete, verified solution with every step shown.
Variance Calculator Formula
s² = Σ(x − x̄)² / (n − 1) (sample), σ² = Σ(x − μ)² / N (population)
Variance measures how spread out data are around the mean: it is the average squared distance from the mean. Divide by n − 1 for a sample (Bessel’s correction) and by N for a whole population. The square root of variance is the standard deviation.
Worked Example
Find the sample variance of 2, 4, 4, 4, 5, 5, 7, 9
- Mean: 40 / 8 = 5
- Squared deviations: 9, 1, 1, 1, 0, 0, 4, 16
- Sum of squares: 32
- Divide by n − 1 = 7: 32 / 7 ≈ 4.571
Answer: s² ≈ 4.571 (population σ² = 4)
Common Mistakes to Avoid
- Dividing by n for a sample, which underestimates the spread.
- Summing the deviations without squaring them (they always sum to zero).
- Reporting variance in the original units — it is in squared units.
How to Use the Variance Calculator Calculator
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Enter your data values or statistical parameters for Variance Calculator
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Variance Calculator formula?
s² = Σ(x − x̄)² / (n − 1) (sample), σ² = Σ(x − μ)² / N (population). Variance measures how spread out data are around the mean: it is the average squared distance from the mean. Divide by n − 1 for a sample (Bessel’s correction) and by N for a whole population. The square root of variance is the standard deviation.
Can you show a worked Variance Calculator example?
Find the sample variance of 2, 4, 4, 4, 5, 5, 7, 9: Mean: 40 / 8 = 5; Squared deviations: 9, 1, 1, 1, 0, 0, 4, 16; Sum of squares: 32; Divide by n − 1 = 7: 32 / 7 ≈ 4.571. Answer: s² ≈ 4.571 (population σ² = 4).
Is this Variance Calculator calculator free to use?
Yes — the Variance Calculator calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Variance Calculator homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.