Mean Median Mode Calculator

What the mean median mode calculator does

The three averages each describe the centre of your data in a different way, and seeing them together tells you more than any one alone. This calculator works out all three at once, the mean, the median, and the mode, and adds the range, the smallest and largest values, the sum, the count, and the sorted list, for a quick snapshot of a data set.

The real value is in the comparison. When the three averages agree, your data is even. When they pull apart, that gap is telling you something, which the sections below get into.

How to use it

1. Enter your numbers in the box, separated by commas, spaces, or new lines.
2. Press Calculate for the full summary, or Reset to clear it.

Mean, median, and mode: which to trust

Each average answers a slightly different question, so the right one depends on what you are asking.

The mean is the arithmetic average, every value added up and divided by the count. It uses all your data, which makes it the standard choice when the numbers are fairly even, but it also means a few extreme values can drag it around. The median is the middle value when the data is sorted. It ignores how far the outer values stretch, so it holds steady when the data is skewed, which is why it is the honest choice for things like income. The mode is the most common value, the right answer when you care about what happens most often, and the only one that works on categories.

For even, well-behaved data, the mean is usually fine. The moment a few values sit far from the rest, lean on the median.

Reading the three together to spot skew

Here is the trick that makes seeing all three at once worthwhile. Compare the mean and the median, and you can read the shape of your data without drawing a thing.

If the mean and median are close, your data is roughly symmetrical, balanced around its centre. If the mean is noticeably higher than the median, the data is skewed to the right, pulled up by some large values in a long upper tail. If the mean is lower than the median, the data is skewed to the left, dragged down by some small values. The mean always moves further than the median in the direction of the skew, because the outliers tug on it and not on the median. So the size and direction of the gap between them is a quick, honest read on which way your data leans.

A worked example: a skewed set

Take five values, in thousands: 20, 25, 25, 30, 100. Think of them as salaries.

• Mean: (20 + 25 + 25 + 30 + 100) ÷ 5 = 200 ÷ 5 = 40
• Median: the middle of the sorted list is 25
• Mode: the most common value is 25

The mean, 40, sits well above the median and mode of 25, even though four of the five values are clustered down at 20 to 30. That single 100 is doing all the lifting. The mean being higher than the median is the signature of a right skew, and it is why the median, 25, is the better description of a typical salary here.

Entering your data, and the rounding

You can separate your numbers with commas, spaces, or new lines, in any mix, and the order does not matter. The range shown here is a single number, the largest value minus the smallest, alongside the smallest and largest themselves. The mean, median, range, and sum are shown to four decimal places with trailing zeros trimmed.

If no value in your data repeats, the mode will read as None, which simply means nothing was more common than anything else. That is normal and does not affect the other figures.

Questions people ask

Which average is best, the mean, median, or mode?

It depends on the data and the question. The mean suits even data, the median suits skewed data with outliers, and the mode tells you the most common value. Seeing all three lets you choose with eyes open.

What does it mean if the mean and median are different?

It points to skew. A mean above the median means the data is skewed right, pulled by large values. A mean below it means skewed left. The closer they are, the more symmetrical the data.

What is the range here?

The largest value minus the smallest, a simple measure of how far the data spreads from end to end. The calculator shows it next to the smallest and largest values themselves.

When are the mean, median, and mode all equal?

When the data is perfectly symmetrical with a single peak, as in a normal distribution. Real data rarely lines up exactly, but the closer the three are, the more balanced your data is.

References

A quick note on where the methods here come from. The definitions of the mean, median, and mode, and the way the gap between the mean and median signals skew, are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook with a clear section on skewness and the three averages.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of location). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (skewness and the mean, median, and mode). https://openstax.org/details/books/introductory-statistics-2e