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.

Variance Calculator σ SD Mean σ+s² SD+Var Solver Sample 🔍 Finder σ² Pop. CV Coeff. CV Var. % % Var Pct. sp² Pooled Poker
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Core Calculators

Standard Deviation Calculator

Calculate standard deviation instantly with step-by-step solutions. Enter your data set and get population SD (σ), sampl…

Core Calculators

Mean Calculator

Calculate the mean (average) of any data set instantly. Get arithmetic mean, along with variance, standard deviation, me…

Relative Measures

Coefficient of Variation Calculator

Calculate the coefficient of variation (CV) instantly. Compare relative variability across data sets with different unit…

Variance Tools

Variance Solver

Solve variance problems instantly with detailed step-by-step solutions. Enter your data set and get sample variance, pop…

Variance Tools

Sample Variance Calculator

Calculate sample variance (s²) instantly with step-by-step solutions. Uses Bessel's correction (n−1) for unbiased estima…

Variance Tools

Variance Finder

Find the variance of any data set instantly. Enter numbers and get both sample and population variance, standard deviati…

Variance Tools

Population Variance Calculator

Calculate population variance (σ²) instantly with step-by-step solutions. Divides by N for exact variance when you have …

Specialized

Poker Variance Calculator

Calculate poker variance and understand your expected results over any number of hands. Analyze win rate variance, downs…

Relative Measures

Coefficient of Variance Calculator

Calculate the coefficient of variance (CV) instantly. Measure relative variability as a percentage of the mean. Get CV, …

Relative Measures

Percentage Variance Calculator

Calculate percentage variance between values or express variance as a percentage of the mean. Get coefficient of variati…

Relative Measures

Percent Variance Calculator

Calculate percent variance of your data set instantly. Express data variability as a percentage using the coefficient of…

Specialized

Pooled Variance Calculator

Calculate pooled variance from multiple groups or samples. Combine sample variances for two-sample t-tests, ANOVA, and m…

Core Calculators

Standard Deviation & Variance Calculator

Calculate both standard deviation and variance instantly. Get population and sample measures with step-by-step solutions…

FAQ

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.