Sample vs. Population Standard Deviation
Population SD is used when your data represents the entire population you're interested in. Sample SD is used when your data is a sample drawn from a larger population — this is the more commonly used version in most real-world statistics, since we rarely have data for an entire population.
The Formulas
Population SD = √[Σ(x − mean)² ÷ n]
Sample SD = √[Σ(x − mean)² ÷ (n − 1)]
Why Sample SD Divides by (n − 1)
This adjustment, known as Bessel's correction, compensates for the fact that a sample's mean is itself an estimate, which tends to make the sample's variance slightly underestimate the true population variance. Dividing by (n−1) instead of n corrects for this bias, giving a more accurate estimate of the population's actual variability.
What Standard Deviation Tells You
Standard deviation measures how spread out your data is from the mean — a small SD means data points cluster tightly around the mean, while a large SD means they're more spread out. It's foundational to many statistical methods, from confidence intervals to hypothesis testing.