What does standard deviation measure?

Standard deviation quantifies the amount of variation or dispersion of a set of values from its mean.

When is median preferred over mean?

Median is preferred when dealing with skewed distributions or datasets containing extreme outliers (such as income or housing prices).

Why divide by (n - 1) for sample variance?

Bessel's correction (n - 1) removes bias when estimating population variance from a finite sample.

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General & Scientific Calculators● INSTANT WASM ENGINE

Statistics Mean, Variance & Standard Deviation Calculator

Statistically analyze numeric distributions with sample mean, population standard deviation (σ), variance, range, and median.

Input Parameters

Dataset Numbers (Comma or Space separated)

Enter raw sample dataset values.

Sample Standard Deviation (s) Instant

±12.16

Mean: 30.00 across 9 samples

Proportional Breakdown100% Total

Mean Value:30.0

Standard Deviation Spread:±12.2

Analytical Summary

Sample Mean (Average)30.00

Sample Median29

Sample Variance (s²)147.75

Dataset Range (Max - Min)12 to 50 (38)

Mathematical Formula & Methodology

Underlying equations and mathematical logic governing this engine

Step 01

Sample Mean (Arithmetic Average)

μ = (Σ x_i) / n

Sum of all observation elements divided by sample size.

Step 02

Sample Variance

s² = Σ (x_i - μ)² / (n - 1)

Average squared deviation around the sample mean.

Step 03

Standard Deviation

s = √s²

Square root of variance measuring dispersion.

How to Use This Calculator

Paste Numeric Sample

Enter data points separated by commas (e.g. 10, 20, 30, 40).

Inspect Distribution Center

Compare mean versus median to evaluate skewness.

Review Dispersion Range

Check standard deviation to measure volatility and spread.