Variance Calculator
Calculate the variance of a dataset.
| Sample | Population | |
|---|---|---|
| Variance | s² = 27.4286 | σ² = 24.0000 |
| Standard Deviation | s = 5.2372 | σ = 4.8990 |
| Count | n = 8 | N = 8 |
| Mean | x̄ = 18.0000 | μ = 18.0000 |
Enter values to see the results.
Variance is a key statistical metric that measures the variability of data from its average. It represents the average of the squared deviations from the mean. This calculator finds the variance for a given data set and illustrates the steps involved.
How to Use This Calculator
Enter your data as a list of numbers separated by commas, spaces, or line breaks. Select whether your data represents a full population or a sample, then click "Calculate." The tool will display the count, mean, sum of squared deviations, variance, and standard deviation.
Population vs. Sample Variance
In statistics, it is crucial to distinguish between a population (all possible observations) and a sample (a subset of the population). The formula for variance differs slightly between the two.
Population Variance (σ²)
Calculated when you have data for the entire population of interest. The formula is:
σ² = Σ(xᵢ - μ)² / N
- μ: The population mean.
- N: The population size.
Sample Variance (s²)
Used when you have data from a sample of the population. The formula is:
s² = Σ(xᵢ - x̄)² / (n - 1)
- x̄: The sample mean.
- n: The sample size.
Steps to Calculate Variance
- Calculate the mean (average) of the data set.
- Subtract the mean from each data point to find the deviation.
- Square each deviation.
- Sum all the squared deviations.
- Divide the sum by N (for population) or n-1 (for sample) to get the variance.
The Significance of Variance
Variance is crucial in fields like finance and science. In investing, it helps assess the risk of an asset—higher variance means higher volatility and risk. Scientists use variance to compare test groups and determine if a hypothesis is valid. While powerful, variance can be skewed by large outliers because squaring the deviations magnifies their effect. For this reason, many researchers prefer to use the standard deviation (the square root of variance), which is easier to interpret.