Variance Calculator

Calculate the variance (sample and population) of any dataset. Understand how spread your data is around the mean. Includes standard deviation.

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📖 How to Use

Step 1: Enter your numbers separated by commas or spaces. Click "Example" for a demo dataset.

Step 2: Click "Calculate" for instant results with box plot and interpretation.

Step 3: Use "Copy" or "CSV" to export results. Click "Recalculate" to try new data.

What Is Variance?

Variance measures how far each value in a dataset is from the mean. It is the average of the squared differences from the mean. A higher variance indicates more spread-out data. The square root of variance is the standard deviation.

Sample vs Population Variance

Population variance (σ²) divides by N: σ² = Σ(x−μ)² / N. Use when your data IS the entire population. Sample variance (s²) divides by N−1: s² = Σ(x−x̄)² / (N−1). Use when your data is a sample from a larger population. The N−1 correction (Bessel's correction) makes the sample variance an unbiased estimator.

❓ Frequently Asked Questions

When do I use N vs N-1?

Use N (population) when you have every member of the group. Use N-1 (sample) when your data is a subset drawn from a larger population, which is most common in practice.

Why is variance squared?

Squaring prevents positive and negative deviations from canceling out. The square root of variance (standard deviation) brings the units back to the original scale.

Variance Calculator

🧮 Calculate Now

📖 How to Use

What Is Variance?

Sample vs Population Variance

❓ Frequently Asked Questions

🔗 Related Calculators

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📈 Statistics (All-in-One)

🔢 Quartile Calculator

📏 IQR Calculator

🎯 Outlier Detection

📦 Box Plot

➗ Mean Calculator

📐 Standard Deviation