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Mean, Median, Mode Calculator

Find the mean, median, mode and range of a list of numbers, with the list sorted and every step shown.

Enter or paste a list of numbers to find the mean, median, mode and range.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

The mean is the ordinary average: add the values and divide by how many there are. The median is the middle value once the list is sorted; with an even number of values it is halfway between the two in the middle. The mode is the value that appears most often, and the range is the highest value minus the lowest.

Paste or type your numbers in any order, separated by commas, spaces or new lines. The calculator sorts them, shows each step, and gives all four answers at once, so you can check your own work line by line.

Every value is read exactly as you typed it, so 0.1, 0.2 and 0.3 average to exactly 0.2. When a mean has a decimal that never ends, such as 25 ÷ 6, it is shown as 4.166666… with the exact fraction alongside, rather than rounded without warning.

For the mode, the calculator follows the rule most US classes teach: if no value repeats, or every value appears the same number of times, there is no mode. If two or more values tie for most frequent, they are all modes, and the data is called bimodal or multimodal.

The formula

Exactly what happens to your numbers, step by step.

Mean

mean = sum of the values
       ÷ number of values

Median

odd count: the middle value
even count: the average of
            the two middle values

Mode and range

mode = the most frequent value
range = highest − lowest

A worked example

Six test scores: 85, 92, 78, 92, 88 and 70.

What you enter

Your numbers: 85, 92, 78, 92, 88, 70

Step by step

Sorted: 70, 78, 85, 88, 92, 92
Mean: 505 ÷ 6 = 84.166666…
Median: (85 + 88) ÷ 2 = 86.5
Mode: 92, which appears twice
Range: 92 − 70 = 22

Mean about 84.17, median 86.5, mode 92, range 22

The median sits above the mean here because one low score, the 70, pulls the average down. That is the usual reason to report a median: a single unusual value moves the mean but barely moves the middle.

Mean, median and mode questions, worked out

The questions that come up most in homework, each answered by the calculator above.

1.Find the mean, median and mode of 3, 7, 7, 2, 9.
1. Put the 5 values in order: 2, 3, 7, 7, 9.
2. Mean: add them up, 3 + 7 + 7 + 2 + 9 = 28, then divide by 5: 28 ÷ 5 = 5.6.
3. Median: with 5 values, the middle one is number 3 in order: 7.
4. Mode: 7 appears twice, more than any other value, so the mode is 7.
Mean 5.6, median 7, mode 7.
2.What is the median of 2, 4, 6, 8?
1. Put the 4 values in order: 2, 4, 6, 8.
2. Median: with 4 values there are two in the middle, numbers 2 and 3. Their average is (4 + 6) ÷ 2 = 5.
5. With an even number of values, the median is the average of the middle two, so it need not be one of the values.
3.What is the mode of 1, 2, 2, 3, 3, 4?
1. Put the 6 values in order: 1, 2, 2, 3, 3, 4.
2. Mode: 2 and 3 each appear twice, more than any other value, so there are two modes.
2 and 3. The data is bimodal: two values tie for most frequent.
4.What is the range of 12, 5, 19, 8?
1. Put the 4 values in order: 5, 8, 12, 19.
2. Range: highest minus lowest, 19 − 5 = 14.
14.
5.Your first three test scores are 80, 90 and 85. What do you need on the fourth for a mean of 87?
1. For a mean of 87 over 4 tests, the scores must add up to 87 × 4 = 348.
2. The first three add up to 80 + 90 + 85 = 255.
3. So the fourth must be 348 − 255 = 93.
4. Check: add them up, 80 + 90 + 85 + 93 = 348, then divide by 4: 348 ÷ 4 = 87.
93.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

Every value counts equally. For a weighted average, such as a grade where the final counts double, use the GPA or final grade calculator instead.
A list with no repeats, or one where every value repeats equally often, has no mode.

What this cannot tell you

Up to 10,000 values. Thousands separators are not allowed, because a comma also separates values: write 1200, not 1,200.
Some textbooks call every value a mode when they all appear equally often. Check which convention your class uses; the calculator says when it applies.
It does not group data into intervals or estimate a mean from a frequency table.

Questions people ask

How do you find the mean, median and mode?

Sort the numbers first. The mean is the total divided by how many there are. The median is the middle number, or the average of the middle two if there is an even count. The mode is whichever number appears most often. For 3, 7, 7, 2 and 9 that gives a mean of 5.6, a median of 7 and a mode of 7.

What if there is an even number of values?

Then there is no single middle value, so the median is the average of the two in the middle. For 2, 4, 6 and 8 the middle two are 4 and 6, so the median is 5, a number that is not in the list at all.

Can a set of numbers have more than one mode, or none?

Yes to both. If two values tie for most frequent, as in 1, 2, 2, 3, 3, 4, both are modes and the data is bimodal. If no value repeats, there is no mode. Most textbooks also say there is no mode when every value appears the same number of times.

When should I use the median instead of the mean?

When a few values are far from the rest. Household incomes and house prices are the classic cases: a handful of very large values pull the mean up, while the median stays with the typical value. For evenly spread data the two are close, and the mean is the usual choice.

Sources and review

Sources

OpenStax, Introductory Statistics, §2.5 — Measures of the Center of the Data (mean, median, mode)

Methodology version 1.0.0 · Last reviewed October 12, 2026

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 12). Mean, Median, Mode Calculator (Methodology version 1.0.0). https://chalkcalculator.com/mean-median-mode-calculator/

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