Sample or population variance?

Variance and σ use the sample formulas with divisor (n−1) — common for coursework (unbiased sample variance).

All ties for highest frequency are listed.

We average the two middle values after sorting.

Spaces and empty tokens are ignored; invalid characters block the run.

● Free & Instant

Summarize Any
Number List

Mean, median, mode, variance, and standard deviation from comma-separated values—ideal for homework & quick QA checks.

Calculate stats ↓

5 Core stats

n−1 Sample σ

List Comma input

Free Instant

Comma-separated numbers

Data

📉

Enter two or more numbers
to see mean, median, mode & spread

Summary

Mean

—

Median

—

Mode(s)

—

Variance (sample)

—

Std dev (sample)

—

Uses divisor (n−1) for variance when n ≥ 2.

How to Use This Calculator

Type numbers separated by commas (spaces optional).
Click calculate to populate mean, median, mode, variance, and standard deviation.
Use sample variance when your list is a subset of a larger population.

📐 Formula

Formula & Methodology

View formula, sources, and explanation+

Mean μ = (Σx)/n
Median: middle of sorted x (average pair if n even)
Mode: value(s) with highest frequency
Sample variance s² = Σ(x−μ)² / (n−1)
Sample σ = √s²

Blank tokens are ignored; all values must parse as JavaScript numbers.

❓ FAQ

Standard Deviation FAQ

When every value appears once, there is no statistical mode—we surface “none.”
This tool emphasizes sample formulas (n−1). Divide by n instead if you truly hold the entire population.
Displayed decimals trim gently—export raw values elsewhere if you need full IEEE precision.
Commas, semicolons, and whitespace all delimit entries.
Nothing uploads.

Summarize AnyNumber List

How to Use This Calculator

Formula & Methodology

Standard Deviation FAQ

Related Calculators

Mean, Median, Mode, Range

Percentage Calculator

Scientific Calculator

Fraction Calculator

Summarize Any
Number List