Sample standard deviation estimates population spread from a sample using n-1 for unbiased estimation.
⚠Sample standard deviation uses n-1 (degrees of freedom). Use population SD for complete datasets.
What is Sample Standard Deviation?
Sample standard deviation (s) is an unbiased estimator of population standard deviation. It measures the spread of sample data around the sample mean.
Sample Mean (x̄)
Average of sample data points used to estimate population mean.
Sample SD (s)
Unbiased estimate of population spread in original units.
Degrees of Freedom
n-1 independent observations available for estimation.
Bessel's Correction
Using n-1 to correct bias in sample estimation.
💡 Example: Sample: 3, 5, 7, 9, 11. Mean = 7, Variance = 10, Std Dev = 3.16.
Applications
Research StudiesMarket SurveysQuality TestingAcademic AnalysisData Science
Frequently Asked Questions
What is sample standard deviation?▼
Sample standard deviation (s) estimates the spread of a population from a sample. It uses n-1 (degrees of freedom) for unbiased estimation. Formula: s = √[Σ(x - x̄)² / (n-1)].
Why use n-1 instead of n?▼
Using n-1 (Bessel's correction) corrects for bias when estimating population parameters from a sample. Without it, the estimate would underestimate the true standard deviation.
When should I use sample standard deviation?▼
Use when you have only a sample of the population, not the entire population. Common in research, surveys, and quality control testing.
What is the difference between s and σ?▼
s is sample standard deviation (estimates population SD from sample). σ is population standard deviation (calculated from entire population). s uses n-1, σ uses N.
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