Standard Deviation Calculator
Calculate standard deviation and variance for a population or sample data set.
Use Sample if your data is a subset of a larger group. Use Population if it represents the entire group.
Understanding Standard Deviation
Standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Formulas
Population Standard Deviation (σ):
σ = √[ Σ(x - μ)² / N ]
Sample Standard Deviation (s):
s = √[ Σ(x - x̄)² / (n - 1) ]
Frequency in Data Science
It is one of the most key metrics in statistics, heavily used in polling, finance (risk measurement), and quality assurance.