Mean, Median and Mode Calculator Guide

What This Calculator Does

Paste a number list to see its count, sum, mean, median, modes, minimum, maximum and range. The mean summarizes the overall level, the median gives the middle sorted position, and modes identify the most frequently repeated values. Each answers a different question.

When to Use It

Use it for observations in the same unit, scores or quantities. Continue to the standard deviation calculator to measure spread. Use weighted grades for course components with different weights; this page gives every observation equal weight.

Inputs Explained

Separate values with commas, spaces, semicolons or new lines. Use a decimal point: 1,5 means two values rather than 1.5. Negative numbers, zero and exponent notation such as 1e3 are accepted. Limits are 10,000 values, 200,000 characters and an absolute magnitude of 1e100 per value.

Unit suffixes, thousands grouping, missing-value labels and expressions are rejected. Invalid observations are not silently removed. Inputs remain in the current page state.

How the Calculation Works

Sum adds every observation; mean divides that sum by the count. Compensated summation reduces cancellation when large positive and negative values offset each other, within floating-point limits.

Median sorts the numbers. For an odd count it uses the middle observation; for an even count it averages the two middle observations. All repeated values tied for the highest frequency are modes, in numeric order. This page reports no mode when every value occurs once; it does not estimate a continuous density peak.

Range = maximum − minimum. Repeats count toward both count and sum. There is no deduplication, outlier removal, quartile convention, IQR or statistical inference.

Example

For 2, 4, 4, 6, 9, count is 5 and sum is 25, so mean is 5. The middle sorted value is 4, so median is 4. The value 4 occurs twice and is the only mode. Minimum is 2, maximum is 9 and range is 7.

For 1, 2, 2, 3, 3, 4, modes are 2 and 3 and median is 2.5. The distinct list 1, 2, 3 has no mode under this page's convention. A single observation 7 has mean and median 7, range 0 and no mode.

How to Understand the Result

Mean, median, modes and range retain the input unit; count is unitless. Results display up to eight decimal places, or scientific notation for very large or small values. Display rounding does not change the calculation. If more than 50 modes tie, only the first 50 are listed with the full tied count; all data still contribute.

Common Mistakes

Entering 1,000 gives observations 1 and 0; write 1000 instead. No mode does not mean no data. Extreme observations influence the mean. This tool cannot decide which values are errors or fill missing observations for you.

FAQ

What if several values have the same highest frequency?

All repeated values tied for highest frequency are modes. If every value occurs once, this calculator reports no mode.

How is the median calculated?

Sort the values. Use the middle value for an odd count, or the mean of the two middle values for an even count.

Can I enter decimal commas or missing values?

Use a dot for decimals. Commas separate values; missing-value labels and expressions are rejected.

Notes

These outputs describe the supplied observations rather than establishing a population distribution, causality or statistical significance. Close large values may lose their difference when parsed into floating-point numbers. See NIST's measures of location for definitions of mean, median and nonunique modes.