Statistics Calculator

Enter a list of numbers to calculate mean, median, mode, standard deviation, and more.

Enter Numbers (comma, space, or newline separated)

Statistics Formulas Reference

Mean: Sum of all values ÷ count
Median: Middle value when sorted (average of two middle values for even count)
Mode: Most frequently occurring value(s)
Range: Maximum − Minimum
Variance: Average of squared deviations from the mean
Standard Deviation: Square root of variance

The Numbers This Tool Returns

Enter a set of numbers and the calculator returns the key descriptive statistics: the mean (average), median (middle value), mode (most frequent), range (max minus min), variance, and standard deviation. Together they describe both the centre of your data and how spread out it is.

Variance and Standard Deviation

Variance measures how far the values sit from the mean on average, by squaring each difference. Standard deviation is the square root of the variance, which brings the figure back to the original units: a small standard deviation means the data clusters tightly around the mean, a large one means it's widely scattered.

Population vs Sample

If your numbers are the entire group you care about, use population variance (divide by n). If they're a sample meant to represent a larger group, use sample variance (divide by n−1), which corrects a slight bias. For a single average, the average calculator is quicker.

Frequently Asked Questions

What is the difference between mean and median?

The mean is the sum divided by count; it's affected by outliers. The median is the middle value; it's more robust to extreme values. For skewed data like income, median is usually more informative.

What does standard deviation tell you?

Standard deviation measures how spread out values are from the mean. A small SD means values cluster tightly around the mean; a large SD means they're spread out.

What is the difference between population and sample standard deviation?

Population SD (σ) divides by N; sample SD (s) divides by N-1. Use sample SD when your data is a subset of a larger population — it corrects for the tendency to underestimate variability.