Variance Calculator

Calculate the variance of a dataset. Enter your numbers separated by commas to find how spread out your data is from the mean.

Quick Facts

What is Variance?
Spread Measure
Measures data dispersion from mean
Population vs Sample
n vs n-1
Sample uses n-1 (Bessel's correction)
Related Measure
Standard Deviation
Square root of variance
Symbol
s² or σ²
Sample or population variance

Your Results

Calculated
Variance
0
Population Variance
Standard Deviation
0
Square root of variance
Mean
0
Average of data

Step-by-Step Calculation

Key Takeaways

  • Variance measures how spread out numbers are from their average (mean)
  • A higher variance indicates data points are more spread out from the mean
  • Population variance divides by n; sample variance divides by n-1
  • Standard deviation is the square root of variance and is in the same units as the data
  • Variance is always non-negative (zero or positive)

What is Variance?

Variance is a statistical measure that quantifies the spread or dispersion of a set of data points around their mean value. It tells you how far each number in the dataset is from the mean and thus from every other number in the set.

In simpler terms, variance answers the question: "How spread out is my data?" A low variance indicates that data points tend to be close to the mean, while a high variance indicates that data points are spread out over a wider range.

The Variance Formula

Population: σ² = Σ(xi - μ)² / N

Sample: s² = Σ(xi - x̄)² / (n - 1)
σ² = Population variance
s² = Sample variance
xi = Each data point
μ or x̄ = Mean
N or n = Number of data points

Population vs Sample Variance

The key difference between population and sample variance is the denominator:

  • Population Variance: Divides by N (total number of data points). Use this when you have data for the entire population.
  • Sample Variance: Divides by n-1 (called Bessel's correction). Use this when your data is a sample from a larger population. The n-1 corrects for the bias in estimating the population variance.

How to Calculate Variance

Follow these steps to calculate variance:

  • Step 1: Calculate the mean (average) of the data set
  • Step 2: Subtract the mean from each data point to get the deviation
  • Step 3: Square each deviation
  • Step 4: Sum all the squared deviations
  • Step 5: Divide by N (population) or n-1 (sample)

Variance vs Standard Deviation

Standard deviation is simply the square root of variance. While variance is expressed in squared units, standard deviation returns to the original units of the data, making it more interpretable. For example, if your data is in dollars, the variance would be in "squared dollars," while the standard deviation would be in dollars.

Applications of Variance

  • Finance: Measuring investment risk and portfolio volatility
  • Quality Control: Monitoring manufacturing consistency
  • Research: Analyzing experimental data variability
  • Weather: Understanding temperature fluctuations
  • Education: Assessing test score distributions