Variance Calculator

Calculate variance for sample and population data with step-by-step solutions.

The Variance Calculator computes the variance of your dataset, measuring how far each number is from the mean. It supports both sample and population variance with step-by-step solutions.

Enter your numbers in the input field
Choose between Sample (n-1) or Population (n) mode
The variance is calculated automatically
Click "Show Steps" to see the squared differences calculation

Both sample (s²) and population (σ²) variance
Step-by-step calculation showing squared differences
Toggle between sample and population modes
Adjustable decimal precision
Summary panel with all descriptive statistics

What is the difference between variance and standard deviation?: Variance is the average of squared differences from the mean. Standard deviation is the square root of variance, expressed in the same units as the original data.
Why is variance always non-negative?: Because it's the sum of squared values, and squares are always non-negative.
When is variance more useful than standard deviation?: Variance is useful in mathematical calculations, particularly in probability theory and analysis of variance (ANOVA).

Enter Data

Data Type

Decimals

Arithmetic Mean

x̄ = (Σxᵢ) / n

Median

Middle value of sorted data

Mode

Most frequent value(s)

Sample Standard Deviation

s = √[Σ(xᵢ - x̄)² / (n - 1)]

Sample Variance

s² = Σ(xᵢ - x̄)² / (n - 1)

Summary Statistics

Count -

Sum -

Min -

Max -

Range -

Mean -

Median -

Mode -

Std Dev (S) -

Std Dev (P) -

Variance (S) -

Variance (P) -

Q1 -

Q2 -

Q3 -

IQR -

Statistics Calculator

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