What is the difference between sample and population formulas?

Sample formulas use a divisor of n − 1 to give an unbiased estimate when your data is a sample from a larger population. Population formulas use n and apply when your data covers the entire population.

How does the calculator pick quartiles?

Q1 and Q3 use linear interpolation between sorted values at the 25th and 75th percentiles (the same method NumPy calls "linear" and Excel calls QUARTILE.INC).

What does "Mode: None" mean?

If no value repeats, no value is more frequent than any other, so there is no mode. The calculator shows None rather than listing every value.

How is excess kurtosis defined?

Excess kurtosis = m4 / σ⁴ − 3, where m4 is the fourth central moment. A normal distribution has excess kurtosis 0; positive means heavier tails.

What happens with non-numeric tokens?

Tokens that fail to parse as numbers are skipped, and the calculator shows a warning so you can see how many were ignored.

Yes — free, no signup, no data leaves your browser.

Statistics Calculator

Compute mean, median, mode, SD, variance, quartiles, IQR, skewness and kurtosis from any list.

Written by Golam Rabbani, Founder & Lead Engineer

This interactive tool requires JavaScript. Read the formula and worked example below; you can compute the result by hand.

How to use this statistics calculator

Paste or type your numbers in the Numbers field, separated by commas, spaces, or newlines.
Press Calculate to compute eighteen descriptive statistics at once.
Read the result table — sample formulas (s, s²) and population formulas (σ, σ²) are reported side by side.
Use Copy to copy every statistic to the clipboard, or Reset to start over.

About this statistics calculator

The statistics calculator returns eighteen descriptive statistics from a single list: count, sum, mean, median, mode, min, max, range, Q1, Q3, interquartile range, sample variance, population variance, sample standard deviation, population standard deviation, standard error of the mean, skewness, and excess kurtosis. Sample formulas use the (n − 1) divisor; population formulas use n. Both are shown so you can pick the right one for your context.

Worked example. Enter 4, 8, 6, 8, 2, 9, 7. Mean = (4+8+6+8+2+9+7) / 7 = 44 / 7 ≈ 6.285714. Sorted: 2, 4, 6, 7, 8, 8, 9, so median = 7 and Q1 = 4, Q3 = 8 (linear interpolation). The mode is 8 (frequency 2). Sum of squared deviations from the mean: (4−6.285714)² + (8−6.285714)² + (6−6.285714)² + (8−6.285714)² + (2−6.285714)² + (9−6.285714)² + (7−6.285714)² = 36.857143. Sample variance s² = 36.857143 / 6 ≈ 6.142857, so s ≈ 2.478479. Population variance σ² = 36.857143 / 7 ≈ 5.265306. Everything runs in your browser — your numbers are never uploaded.

FAQ

What is the difference between sample and population formulas?: Sample formulas use a divisor of n − 1 to give an unbiased estimate when your data is a sample from a larger population. Population formulas use n and apply when your data covers the entire population.
How does the calculator pick quartiles?: Q1 and Q3 use linear interpolation between sorted values at the 25th and 75th percentiles (the same method NumPy calls "linear" and Excel calls QUARTILE.INC).
What does "Mode: None" mean?: If no value repeats, no value is more frequent than any other, so there is no mode. The calculator shows None rather than listing every value.
How is excess kurtosis defined?: Excess kurtosis = m4 / σ⁴ − 3, where m4 is the fourth central moment. A normal distribution has excess kurtosis 0; positive means heavier tails.
What happens with non-numeric tokens?: Tokens that fail to parse as numbers are skipped, and the calculator shows a warning so you can see how many were ignored.
Is this tool free?: Yes — free, no signup, no data leaves your browser.