Variance - Variance Formula
This free online tool helps you calculate variance using the variance formula for population and sample data sets. It explains variance meaning and variance definition while showing how to calculate variance with step-by-step results. Use it to understand what is variance and interpret your statistical data with confidence.
Input Data
Supports integers and decimals. Separate values with commas, spaces, or newlines
Calculation Results
Variance Formula - Definition, Meaning and How to Calculate Variance
First, understand the definition of variance: variance is a statistical measure of how far a set of numbers is spread out from their average. The variance meaning in statistics reflects data dispersion; a higher variance indicates greater spread, while a lower variance means data points are more concentrated around the mean. You can calculate variance using the variance formula for population or sample data sets.
What Is Variance in Statistics?
Variance is a statistical measure of the dispersion of data points around the mean. The variance definition can be stated as the average of the squared differences from the mean. In statistics, variance meaning is closely related to standard deviation; variance is the square of the standard deviation and has squared units relative to the original data.
The variance formula for a population is σ² = Σ(xᵢ - μ)² / N, where μ is the population mean and N is the total number of data points. For a sample, the sample variance formula uses n-1 as the denominator to provide an unbiased estimate: s² = Σ(xᵢ - x̄)² / (n - 1).
Sample Variance Formula and Formula for Variance
Formula for variance depends on whether you are working with a population or a sample. For a population, use σ² = Σ(xᵢ - μ)² / N. For a sample, use the sample variance formula s² = Σ(xᵢ - x̄)² / (n - 1), where x̄ is the sample mean and n is the sample size.
σ² = Σ(xᵢ - μ)² / N (Population Variance Formula)
s² = Σ(xᵢ - x̄)² / (n - 1) (Sample Variance Formula)
How to Calculate Variance and How to Find Variance
To calculate variance, first find the mean of your data set. Then subtract the mean from each data point, square the result, and sum all squared differences. For a population, divide by the total number of data points; for a sample, divide by n-1. This is how to find variance using the standard variance formula.
- Population Variance (σ²): Used when you have data for the entire group you want to study (denominator = N)
- Sample Variance (s²): Used when you only have a subset of data and want to estimate population parameters (denominator = n-1, Bessel's correction)
- Sample variance uses n-1 to correct for bias in estimating population variance from a sample
- Standard deviation has the same units as the original data, while variance has squared units
How to Use This Variance Calculator
- Enter your numerical data set (supports commas, spaces, or newlines as separators)
- Select the calculation type: Population or Sample
- Choose your desired precision (decimal places for results)
- Click "Calculate Variance" to get instant results
- View detailed step-by-step calculations to understand how results are derived
- Copy the summary results for your records or further analysis
Variance FAQ
- What does variance mean? Variance measures the average squared deviation of each number from the mean. A higher variance means data points are more spread out; a lower variance means they are closer together.
- How to find variance? Subtract the mean from each data point, square the differences, sum them, and divide by N for population or n-1 for sample.
- What is variance in statistics? In statistics, variance is a measure of dispersion that quantifies how far a set of numbers is spread out from their average value.
- Formula for variance is σ² = Σ(xᵢ - μ)² / N for population and s² = Σ(xᵢ - x̄)² / (n - 1) for sample.
- Sample variance formula uses n-1 in the denominator to correct for bias when estimating population variance from a sample.