Calculate both population and sample variance with their standard deviations to measure data spread.
Last updated: March 2026
Variance is a statistical measure that quantifies how much a set of numbers varies or spreads out from their average value (mean). It represents the average of the squared differences from the mean, providing a numerical value that indicates data dispersion.
There are two types of variance: population variance (σ²) which divides by N (the total number of values), and sample variance (s²) which divides by N-1. Population variance is used when you have data for an entire population, while sample variance is used when working with a sample from a larger population. The N-1 denominator in sample variance (called Bessel's correction) provides an unbiased estimate of the population variance.
Variance is fundamental in statistics and appears in many statistical tests and procedures. The square root of variance gives you the standard deviation, which is often easier to interpret because it's in the same units as your original data. High variance indicates data points are spread far from the mean, while low variance indicates they cluster closely around it.
Calculate variance for test scores:
Population variance (σ²) divides by N and is used when you have all data. Sample variance (s²) divides by N-1 and is used when estimating from a sample. The N-1 correction makes sample variance an unbiased estimator of population variance.
Squaring prevents positive and negative differences from canceling out, ensures all values are positive, and gives more weight to larger deviations. This mathematical property makes variance useful in many statistical analyses.
Use variance for mathematical calculations in statistics (like ANOVA). Use standard deviation for interpretation because it's in the same units as your data. Standard deviation is just the square root of variance.
High variance means data points are spread far from the mean—there's high variability. Low variance means data is clustered tightly around the mean—there's consistency. Zero variance means all values are identical.
This is Bessel's correction. Using N-1 (degrees of freedom) instead of N corrects for bias that occurs when estimating population variance from a sample. It produces an unbiased estimate of the true population variance.
No, variance is always zero or positive because it's the average of squared values. A variance of zero means all values are identical. Larger variances indicate greater spread in the data.
Variance is used in portfolio risk analysis, quality control, hypothesis testing (t-tests, ANOVA), regression analysis, designing experiments, and anywhere you need to quantify uncertainty or variability in data.
Outliers greatly affect variance because differences are squared. A single extreme value can dramatically increase variance. This is why variance is sensitive to outliers—consider using robust measures like interquartile range if outliers are problematic.
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