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Sample: Use when data is a subset of the population (divide by n-1)
Variance measures how spread out data is from the mean. It's the average of squared deviations from the mean.
Formula
σ² = Σ(xᵢ - μ)² / N (population) or s² = Σ(xᵢ - x̄)² / (n-1) (sample)
Squaring ensures all deviations are positive. Sample variance uses n-1 (Bessel's correction) for unbiased estimation.
Use population variance when you have all data points; sample variance when analyzing a subset.
Variance is in squared units. For original units, use standard deviation.
Outliers greatly inflate variance since deviations are squared.
Manufacturing uses variance to monitor process consistency.
Variance measures investment risk and portfolio volatility.
ANOVA uses variance to compare group means.
Bessel's correction accounts for estimating the mean from the sample, making it unbiased.
Standard deviation = √variance. It's in the same units as the data, making it more interpretable.
Data points are spread far from the mean. Low variance means data clusters near the mean.
CV = (standard deviation / mean) × 100%. It expresses variability as a percentage of the mean.