Formulas
Mean (μ) = ∑x / n
Population variance (σ²) = ∑(x − μ)² / n
Sample variance (s²) = ∑(x − μ)² / (n − 1)
Standard deviation = √variance
Population mode divides by n (when data is the entire population). Sample mode divides by n−1 (Bessel's correction, when data is a sample).
FAQ
When should I use population vs sample?
Use population if your data represents the entire group. Use sample if your data is a subset of a larger group (most common in practice).
What does standard deviation tell me?
It measures how spread out the data is from the mean. A low SD means data points are close to the mean; a high SD means they are spread out. About 68% of data falls within 1 SD of the mean in a normal distribution.