Sample variance estimates population variance from a sample using n-1 to correct estimation bias.
⚠Sample variance uses n-1 (degrees of freedom) in the denominator, not n. This is Bessel's correction for unbiased estimation.
What is Sample Variance?
Sample variance (s²) is an unbiased estimator of the population variance. When you only have a sample (not the entire population), it estimates how spread out the population data is.
Sample Mean (x̄)
The average value of the sample data. x̄ = Σx / n
Sample Variance (s²)
Unbiased estimate of population variance using n-1.
Bessel's Correction
Using n-1 instead of n to correct estimation bias.
Degrees of Freedom
n-1 independent observations available for estimation.
💡 Example: Sample: 3, 5, 7, 9, 11, 13. Mean = 8, Variance = 14, Std Dev = 3.74.
Applications
Market ResearchScientific StudiesQuality TestingSurveysAcademic Research
Frequently Asked Questions
What is sample variance?▼
Sample variance (s²) estimates the variance of a population from a sample. It uses n-1 (degrees of freedom) in the denominator to correct bias. Formula: s² = Σ(x - x̄)² / (n-1).
Why do we use n-1 for sample variance?▼
Using n-1 (Bessel's correction) corrects for bias when estimating population variance from a sample. Without it, the estimate would systematically underestimate the true population variance.
When should I use sample variance?▼
Use sample variance when you only have a subset (sample) of the population data. This is common in research, surveys, and quality control where measuring the entire population is impractical.
What is degrees of freedom?▼
Degrees of freedom (df = n-1) represents the number of independent observations in the sample that can vary freely when estimating population parameters from sample data.
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