Variance Calculator
Calculate the variance of a dataset used to measure feature spread in ML pipelines.
Inputs
Separate values with commas or spaces.
Sample Variance
182.0000
Population Variance
151.6667
Mean
18.0000
Count (n)
6
Step by step
Mean
Σx ÷ 6
= 18.0000
Sum of squared deviations: Σ(x − mean)²
= 910.0000
Sample variance: Σ(x−mean)² ÷ (n−1)
÷ 5
= 182.0000
Population variance: Σ(x−mean)² ÷ n
÷ 6
= 151.6667
How it works
Variance measures how spread out a dataset is around its mean: var = Σ(x − mean)² / n for the population variance, or Σ(x − mean)² / (n−1) for the sample variance. The (n−1) divisor (Bessel's correction) makes the sample variance an unbiased estimator of the true population variance when working from a sample. In ML, variance is central to feature scaling, understanding model output stability (variance in predictions across bootstrap samples), and diagnosing overfitting via the bias-variance tradeoff.
Formulas
Sample variance
s^2 = sum((x_i - mean)^2) / (n - 1)
- x_i
- Individual data values
- mean
- Arithmetic mean of the dataset
- n
- Number of values
Population variance
sigma^2 = sum((x_i - mean)^2) / n
- x_i
- Individual data values
- mean
- Arithmetic mean of the dataset
- n
- Number of values
Frequently Asked Questions
When should I use sample vs. population variance?
Use sample variance (÷ n−1) when your data is a subset drawn from a larger population — the common case in ML datasets; use population variance (÷ n) only when your data represents the entire population of interest.
Why does the sample variance divide by n−1 instead of n?
Dividing by n tends to underestimate the true population variance when using the sample mean (rather than the unknown true mean) in the calculation; dividing by n−1 corrects this bias, which is known as Bessel's correction.
How is variance related to standard deviation?
Standard deviation is simply the square root of variance — variance is in squared units of the original data, while standard deviation is in the same units, making it easier to interpret directly.
How is variance used in the bias-variance tradeoff?
In ML, 'variance' in this context refers to how much a model's predictions change across different training sets — high-variance models (like deep decision trees) overfit noise, while high-bias models (like linear regression on nonlinear data) underfit; the mathematical variance computed here is the building block for that broader concept.