Statistics Dictionary

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Randomization Randomized Block Design Randomized Block Experiment Range Ratio Scale Reduced Row Echelon Form Region of Acceptance Region of Rejection Regression Relative Frequency Relative Frequency Table Repeated Measures Design Replication Representative Residual Residual Plot Response Bias Row Echelon Form Row Vector Sample Sample Design Sample Point Sample Space Sample Survey Sampling Sampling Distribution Sampling Error Sampling Fraction Sampling Method Sampling With Replacement Sampling Without Replacement Scalar Matrix Scalar Multiple Scatterplot Scheffe Test Selection Bias Set Significance Level Simple Random Sampling Simple Regression Singular Matrix Skewness Slope Sphericity Standard Deviation Standard Error Standard Normal Distribution Standard Score Statistic Statistical Experiment Statistical Hypothesis Statistics Stemplot Strata Stratified Sampling Subset Subtraction Rule Sum Vector Sums of Squares Symmetric Matrix Symmetry Systematic Sampling T Distribution T Score T Statistic Test Statistic Transpose Treatment t-Test Two-Sample t-Test Two-stage Sampling Two-Tailed Test Two-Way Table Type I Error Type II Error Unbiased Estimate Undercoverage Uniform Distribution Unimodal Distribution Union Univariate Data Variable Variance Variance Inflation Factor Vector Inner Product Vector Outer Product Vectors Venn Diagram Voluntary Response Bias Voluntary Sample Y Intercept z-score

Variance

The variance is a numerical value used to indicate how widely individuals in a group vary. If individual observations vary greatly from the group mean, the variance is big; and vice versa.

It is important to distinguish between the variance of a population and the variance of a sample. They have different notation, and they are computed differently. The variance of a population is denoted by σ²; and the variance of a sample, by s².

The variance of a population is defined by the following formula:

σ² = Σ ( X_i - X )² / N

where σ² is the population variance, X is the population mean, X_i is the ith element from the population, and N is the number of elements in the population.

The variance of a sample is defined by slightly different formula:

s² = Σ ( x_i - x )² / ( n - 1 )

where s² is the sample variance, x is the sample mean, x_i is the ith element from the sample, and n is the number of elements in the sample. Using this formula, the variance of the sample is an unbiased estimate of the variance of the population.

And finally, the variance is equal to the square of the standard deviation.

See also:

Statistics Tutorial: Measures of Variability | AP Statistics Tutorial: Measures of Variability | Random Variable Attributes