Mode Calculator

What the mode calculator does

The mode is the value that shows up most often in your data. This calculator finds it, and builds a frequency table showing how many times each value appears, so you can see the whole picture, not just the winner.

It is the only one of the three averages that points to an actual, repeated value in your set, and the only one that works on things you cannot add up, like sizes or choices. Below is how it works, including what happens when there is a tie, or nothing repeats at all.

How to use it

1. Enter your numbers in the box, separated by commas, spaces, or new lines.
2. Press Calculate to see the mode and the frequency table, or Reset to clear it.

How the mode is found

The calculator counts how many times each value appears, then picks out the value with the highest count. That is the mode.

Two things can happen along the way. If two or more values are tied for the most appearances, they are all modes, and the calculator lists every one of them, a set of data being perfectly allowed to have more than one mode. And if no value repeats, if every number appears exactly once, then there is no most-common value, so the result is simply None. Both of these are normal, and the frequency table shows the counts behind whichever you get.

When the mode is the right average

The mode earns its keep when the question is which is most common, rather than what is the middle or the average size. The most popular shirt size to stock, the most frequent score on a quiz, the answer most people chose in a survey: these are mode questions, and neither the mean nor the median can answer them.

It is also the only average that works on categories. You cannot add up or sort colours, or shoe styles, or brand names to find a mean or a median, but you can still count which one comes up most. That makes the mode the natural summary for that kind of data, where the values are labels rather than numbers.

Worked examples: one mode, two modes, none

The set 2, 4, 4, 4, 7, 9 has one clear winner. The value 4 appears three times and everything else appears once, so the mode is 4.

The set 2, 2, 5, 5, 8 has a tie. Both 2 and 5 appear twice, more than anything else, so there are two modes, 2 and 5. Data like this is called bimodal.

The set 1, 2, 3, 4 has no repeats at all. Every value appears exactly once, so there is no most-common value and the result is None.

The frequency table, and entering your data

Alongside the mode, the calculator shows a frequency table: every distinct value in your data, sorted, with the number of times it appears. It is worth a look even when you only wanted the mode, because it shows the shape of your data at a glance, which values cluster and which stand alone.

You can separate your numbers with commas, spaces, or new lines, and the order does not matter. The calculator handles sets from two numbers up to five hundred, which covers all but the largest pastes.

Questions people ask

What is the mode?

The value that appears most often in a set of data. It is one of the three common averages, with the mean and the median, and the only one that always lands on a value actually in your data.

Can a data set have more than one mode?

Yes. If two or more values tie for the most appearances, they are all modes. Two modes is called bimodal, and more than two is multimodal.

What if no number repeats?

Then there is no mode, and the calculator returns None. With every value appearing once, no single value is more common than the others.

What is the mode used for?

For finding the most common value, and for summarising categories you cannot average, like sizes, colours, or survey choices. In those cases it is the only average that applies.

References

A quick note on where the methods here come from. The definition of the mode and its place among the measures of central tendency 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 that covers the mode and the kinds of data it suits.

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