Mean, median and mode calculator

Paste a list of numbers to find the mean, median, mode and range, with each one worked out step by step.

  • Free, no sign-up
  • Step-by-step working
  • Runs in your browser

Separate values with commas, spaces or new lines. You can paste a column from Excel or Google Sheets.

How to use the mean, median and mode calculator

  1. Type or paste your numbers into the box. Commas, spaces, tabs and new lines all work, so you can paste a column straight from a spreadsheet.
  2. Click Calculate. The mean, median and mode appear at the top, along with the range.
  3. Check the dot plot: each dot is one value, stacked when values repeat, with the mean and median marked.
  4. Read What this means to see whether your data are skewed and which average describes them best.
  5. Follow the step-by-step working to see exactly how each answer was reached, or download the chart.

Mean, median and mode formulas

Mean: x = Σxn

Median (n odd): the value in position n + 12

Median (n even): the average of the values in positions n2 and n2 + 1

Range: largest value − smallest value

x
The mean (arithmetic average) of the sample
Σx
The sum of all the values
n
How many values there are
Position
A place in the list after sorting from smallest to largest; position 1 is the smallest value
Mode
The value (or values) that occur most often. There is no formula: count how many times each value appears

Worked example

A class of seven students scores 82, 75, 90, 75, 88, 95 and 70 on a quiz. Find the mean, median and mode.

  1. Sort the scores from smallest to largest
    70, 75, 75, 82, 88, 90, 95
  2. Mean: add the scores and divide by 7
    x = 70 + 75 + 75 + 82 + 88 + 90 + 957 = 5757 = 82.14
  3. Median: n = 7 is odd, so take the value in position (7 + 1) / 2 = 4
    Median = 82
  4. Mode: 75 appears twice; every other score appears once
    Mode = 75
  5. Range: largest minus smallest
    Range = 95 − 70 = 25

What it means: the mean (82.14) and median (82) are almost identical, so the scores are fairly balanced around the center with no extreme values pulling the average. A typical student scored about 82. The mode, 75, only tells you that two students happened to get the same score; with small data sets the mode is often not very informative.

How to interpret the mean, median and mode

  • Mean ≈ median: the data are roughly symmetric. The mean is a good summary and works well with other statistics like the standard deviation.
  • Mean > median: the data are likely skewed to the right, with a long tail of large values. Common for incomes, prices, waiting times and website traffic. The median is a better "typical" value.
  • Mean < median: the data are likely skewed to the left, with a tail of small values, such as scores on an easy test where most people do well.
  • The mode is most useful for data with many repeated values, such as shoe sizes, survey ratings or the number of children per family. It is the only one of the three that works for categories (like favorite color).

The center is only half the story. Two data sets can share the same mean but have very different spreads, so pair these results with the standard deviation, and use a histogram to see the full shape of the data.

Frequently asked questions

What is the difference between the mean, median and mode?

All three describe the center of a data set in different ways. The mean is the arithmetic average: add everything up and divide by how many values there are. The median is the middle value once the data are sorted. The mode is the value that appears most often. In a perfectly symmetric distribution they are all equal.

Which is better, the mean or the median?

Use the mean for roughly symmetric data without extreme values, because it uses every observation. Use the median when the data are skewed or contain outliers, such as incomes, house prices or response times, because a few very large values pull the mean up but barely move the median. Reporting both is often the most honest choice.

How do you find the median of an even set of numbers?

Sort the values, then take the two middle values and average them. For 3, 5, 8, 10 the middle values are 5 and 8, so the median is (5 + 8) / 2 = 6.5. With an odd count, the median is simply the single middle value.

Can a data set have more than one mode, or no mode?

Yes. If two values tie for the highest count, the data are bimodal; with more, they are multimodal. If every value appears the same number of times (for example, all values are different), there is no mode. The calculator lists every mode it finds and tells you when there is none.

What does it mean when the mean is larger than the median?

It usually means the data are skewed to the right: a few large values in the upper tail pull the mean upward. When the mean is smaller than the median, the data are usually skewed to the left. A histogram makes the shape easy to see.

What is the range?

The range is the largest value minus the smallest value. It is a quick measure of spread, but it depends only on the two most extreme values. For a measure of spread that uses all the data, use the standard deviation.

Last reviewed November 10, 2026