Variance Solver
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13 specialized statistical calculators — each with personalized step-by-step solutions, formulas, and FAQs. Pick the tool that fits your problem.
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Mean Calculator
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Coefficient of Variation Calculator
Calculate the coefficient of variation (CV) instantly. Compare relative variability across data sets with different unit…
Variance Solver
Solve variance problems instantly with detailed step-by-step solutions. Enter your data set and get sample variance, pop…
Sample Variance Calculator
Calculate sample variance (s²) instantly with step-by-step solutions. Uses Bessel's correction (n−1) for unbiased estima…
Variance Finder
Find the variance of any data set instantly. Enter numbers and get both sample and population variance, standard deviati…
Population Variance Calculator
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Coefficient of Variance Calculator
Calculate the coefficient of variance (CV) instantly. Measure relative variability as a percentage of the mean. Get CV, …
Percentage Variance Calculator
Calculate percentage variance between values or express variance as a percentage of the mean. Get coefficient of variati…
Percent Variance Calculator
Calculate percent variance of your data set instantly. Express data variability as a percentage using the coefficient of…
Pooled Variance Calculator
Calculate pooled variance from multiple groups or samples. Combine sample variances for two-sample t-tests, ANOVA, and m…
Standard Deviation & Variance Calculator
Calculate both standard deviation and variance instantly. Get population and sample measures with step-by-step solutions…
Frequently Asked Questions — Variance Solver
Everything you need to know about variance.
How do you solve for variance?
To solve for variance: 1. Find the mean (x̄ = Σxᵢ / n). 2. Subtract the mean from each value to get deviations. 3. Square each deviation. 4. Sum all squared deviations. 5. Divide by n (population) or n−1 (sample). Our solver shows every step with your actual numbers, making it easy to follow and verify.
How to solve variance of 2, 4, 6, 8, 10?
For 2, 4, 6, 8, 10: Mean = 30/5 = 6. Deviations: −4, −2, 0, 2, 4. Squared: 16, 4, 0, 4, 16. Sum of squares = 40. Population variance (σ²) = 40/5 = 8. Sample variance (s²) = 40/4 = 10. Standard deviation: σ = √8 ≈ 2.828, s = √10 ≈ 3.162.
What does a high variance mean?
High variance means data points are widely spread from the mean. The numbers in your data set differ significantly from each other and from the average. In finance, high variance indicates volatile investments. In manufacturing, high variance signals inconsistent production. In test scores, high variance means students performed very differently from each other.
Can I solve variance with only two numbers?
Yes, you can calculate population variance with just 1 or more values (variance of a single number is 0). For sample variance, you need at least 2 values because the formula divides by n−1, and dividing by zero (when n=1) is undefined. With two values like 3 and 7, the mean is 5, and the sample variance is [(3−5)² + (7−5)²] / 1 = 8.
What is the variance formula for grouped data?
For grouped data (frequency distributions), use the weighted variance formula: σ² = Σ[fᵢ(xᵢ − x̄)²] / N, where fᵢ is the frequency of each value, xᵢ is the midpoint, and N = Σfᵢ is the total frequency. First find the weighted mean: x̄ = Σ(fᵢ · xᵢ) / N. Then compute the weighted sum of squared deviations.
Why does the variance formula square the differences?
Squaring serves two purposes: 1. It eliminates negative signs — without squaring, positive and negative deviations would cancel out, giving a misleading result of zero. 2. It gives more weight to larger deviations, making variance sensitive to outliers. The trade-off is that variance is in squared units, which is why we often take the square root to get standard deviation.