Math calculator

Free mean median mode range calculator

Find the mean, median, mode, and range of a dataset — enter a list of numbers and get all four descriptive statistics at once, updated live, as you type.

On this page10 sections

InputsLive

Numbers (comma-separated)

Enter numbers separated by commas or spaces.

Result

Mean

Median = 3, N = 7

Mean4

Median3

Mode2

Range8

Min1

Max9

Mean = sum÷N; median = middle value; mode = most frequent; range = max−min.

Results are estimates. Consult a professional.

How it's calculated

How the mean, median, mode & range calculator works

These four measures summarise a data set from different angles. Mean gives the arithmetic average; median gives the middle value; mode gives the most frequent value; range measures the spread.

Mean = Σx / n

Median = middle value (or average of two middle values when n is even)

Mode = value that appears most often

Range = maximum value − minimum value

National Institute of Standards and Technology — Engineering Statistics Handbook

Example

Worked example: 15-value data set

Example: {3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29}

Sort the data: 3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56 (n = 15).

Mean = (3+5+7+12+13+14+20+23+23+23+23+29+39+40+56) / 15 = 330 / 15 = 22

Median = 8th value = 23 (middle of 15 sorted values)

Mode = 23 (appears 4 times)

Range = 56 − 3 = 53

Mean 22 · Median 23 · Mode 23 · Range 53

The mean is pulled slightly below the median by the cluster of low values (3–14), a sign of mild left skew.

Quick reference

When to use mean, median, or mode

Choosing the right measure of centre depends on your data's distribution and what question you are answering.

Measure	Best used when	Sensitive to outliers?
Mean	Data is roughly symmetric, no extreme outliers	Yes — greatly
Median	Data is skewed or contains outliers (e.g. incomes)	No — robust
Mode	Finding the most common category or value	No
Range	Quick gauge of total spread	Yes — uses only max & min

Source: Khan Academy Statistics & Probability

Practical tips

Tips for analysing data sets

Getting accurate results starts with clean, consistently formatted data. Keep these points in mind.

Sort before finding the median — arrange values from smallest to largest first; for even-count sets, average the two middle values.
A data set can have no mode — if every value appears exactly once, the set is said to have no mode (or is "amodal").
Multiple modes are valid — bimodal (two modes) or multimodal sets are common in real-world data.
Range alone is not enough — two sets can share the same range yet have very different distributions; pair it with standard deviation for more insight.
Remove entry errors first — a single typo (e.g. 2300 instead of 23) can skew the mean dramatically; always verify outliers before calculating.

Accuracy & limits

Accuracy and limitations

This calculator computes exact values for integer and decimal inputs up to 15 significant digits (IEEE 754 double precision). For extremely large data sets or values with many decimal places, rounding at the 15th digit may occur. The four measures here are descriptive statistics only — they describe the sample you enter, not a population. For inferential statistics (confidence intervals, hypothesis tests) use a dedicated statistical tool.

Glossary

Key terms

The sum of all values divided by the count of values; the arithmetic average.

The middle value of a sorted data set; splits the data into two equal halves.

The value (or values) that occur most frequently in a data set.

The difference between the maximum and minimum values; a basic measure of spread.

A data point that lies far from the rest of the distribution, often distorting the mean.

Asymmetry in a distribution; positive skew pulls the mean above the median, negative skew pulls it below.

About

About this calculator

Part of our math calculators suite — explore all calculators.

Questions

Frequently asked questions about the free mean median mode range calculator

A mean median mode range calculator is a free online tool that helps you all four basic 'averages' of a dataset in one calculation — mean, median, mode(s), and range. These four are the foundational descriptive statistics. Each summarizes a different aspect of the data — center (mean, median, mode) or spread (range). It runs entirely in your browser with instant results and no sign-up.

When the data has outliers or is skewed. Median is the middle value, so a few extreme values don't shift it much. Mean is more efficient when the data is symmetric without outliers.

One with two modes — two values that tie for most frequent. The calculator returns all tied modes. A dataset can also be trimodal, multimodal, or have no mode at all.

It's the simplest but the least robust. Range only uses two values (max and min), so a single outlier can dominate it. Standard deviation gives a more stable picture of spread for most analyses.