Variance Calculator

Variance is a measure of how spread out a set of data is from its mean. It represents the average of the squared differences from the mean, giving you a numerical value that describes the variability in your data set.

Population variance divides by n (total number of values) and is used when you have data for the entire population. Sample variance divides by n-1 (Bessel's correction) and is used when you have a sample of a larger population. The n-1 divisor provides an unbiased estimate of the population variance.

Sample variance: s^2 = Σ(xi - x̄)^2 / (n-1), where xi represents each value, x̄ is the mean, and n is the number of values. Population variance: σ^2 = Σ(xi - μ)^2 / n, where μ is the population mean.

Standard deviation is the square root of variance. While variance is expressed in squared units, standard deviation is in the same units as the original data, making it more interpretable. Both measure variability, but standard deviation is often preferred for interpretation.

Use population variance when you have data for the entire population you're studying. Use sample variance when you have a subset (sample) of a larger population and want to estimate the population variance. In most real-world scenarios, you'll use sample variance.

No, variance can never be negative because it's calculated as the average of squared differences. Squared numbers are always positive or zero, so variance is always non-negative. A variance of zero means all values in the dataset are identical.