Sample Variance vs Population Variance

Last Updated : 6 Feb, 2026

Sample and Population variance are two essential measures in statistics used to quantify the spread or variability of data points in a dataset. Population variance measures how spread out the values are in an entire group (or population). On the other hand, sample variance is used when we have only a part of the group (a sample) and want to estimate the variance of the whole group.

Variance

Variance is a statistical measure that represents the degree of spread or dispersion in a set of values. In other words, it quantifies how much the numbers in a dataset differ from the mean (average) of the dataset. It helps us understand the spread or variability in our data.

  • Sample Variance
  • Population Variance

Differences Between Sample and Population Variance

AspectSample Variance ( s2 )Population Variance ( σ2 )
DefinitionMeasure of dispersion in a sampleMeasure of dispersion in an entire population
Formula

s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2

\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2

Mean UsedSample mean (\bar{x})Population mean (μ)
Denominatorn − 1 (degrees of freedom)N (total number of data points)
PurposeEstimates the population variance from a sampleMeasures the true variance of the population
Bias AdjustmentDividing by n − 1 corrects the bias in estimationNo bias adjustment needed, uses entire population data
UsageWhen only a subset of the population is availableWhen the entire population data is available
Data SetSample data (a subset of the population)Population data (all data points in the population)

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