Statistics & Standard Deviation Calculator

Calculate Mean, Median, Mode, Sample & Population Standard Deviation, Variance, Min, Max, Range, and Quartiles.

Configurable Calculation Inputs

Dataset (Comma or Space Separated): text (Default: 12, 18, 22, 24, 25, 29, 31, 35, 40, 48)

Mathematical Formula: Sample Standard Deviation & Mean Equations

          Mean (x̄) = Σx / N ; Sample StdDev (s) = sqrt[ Σ(x - x̄)² / (N - 1) ]
        

Calculates central tendency and dispersion metrics for arbitrary dataset samples and full populations.

Comprehensive Guide & Context

Empirical Rule for Normal Distributions

68% of data points fall within 1 standard deviation of the mean, 95% fall within 2 standard deviations, and 99.7% fall within 3 standard deviations.

Worked Calculation Examples

Test Exam Score Distribution

Scores: 78, 85, 92, 65, 88, 90, 72, 95.

Result: Mean: 83.13 · Std Dev: 10.15

Frequently Asked Questions

When should I use Sample vs Population Standard Deviation?

Use Sample Standard Deviation (divided by N-1) when analyzing a sample dataset to estimate the broader population. Use Population (divided by N) when your data represents the entire complete universe.