Mode Calculator

What is the mode?

The mode of a data set is the value that occurs most often. It is the only measure of central tendency that also makes sense for categories such as colours, brands or answer choices, because finding it needs counting rather than arithmetic.

Where the mean and median describe the centre of the data, the mode describes its most popular point. In a histogram it is the tallest bar, and a distribution with one clear peak is called unimodal.

How to find the mode

1. List the distinct values that appear in the data.
2. Count how many times each one occurs.
3. The value with the highest count is the mode. If several share the highest count, all of them are modes.

Example: a shoe shop records the sizes sold in a day: 8, 9, 9, 7, 10, 9, 8, 11 and 9. Tallying gives size 7 once, size 8 twice, size 9 four times, size 10 once and size 11 once. Size 9 has the highest tally, so the mode is 9, and it is the size worth keeping the most stock of.

How the calculator reads your list

• Numbers can be separated by commas, spaces, tabs or new lines; empty gaps between separators are skipped.
• Values are compared by their whole-number part. 2.5 and 2.7 both count as 2, and the mode is reported as 2. If your decimals matter, round them to the precision you care about, or multiply by 10 or 100, before you enter them.
• When several values tie, they are listed in the order in which they first appear in your list, and the row is labelled with how many were found.
• Anything that is not a number is read as zero and counted. A semicolon is not a separator, so 1;2;2;3 is read as the single number 1223.
• The second row, Count of numbers, shows how many entries were read, which is a quick way to catch a typo.

Mode compared with mean and median

For a symmetric, single-peaked distribution the mode, median and mean land on the same spot. For a right-skewed distribution, such as incomes, the mean usually exceeds the median and the median usually exceeds the mode, because the long tail pulls the larger averages upward. Left-skewed data tends to reverse that order.

The mode is not affected by extreme values at all, but it can be unstable: adding one more observation to a close race can move it to a different value. When you need a measure of the middle, use the median calculator; for the arithmetic average, use the mean calculator; and to see all of them together, try the mean, median and mode calculator.

Where the mode is useful

• Retail and stock: the most common size, colour or pack quantity sold.
• Surveys: the rating or answer chosen by the largest number of respondents. Code the answers as numbers (1 to 5, for instance) before entering them.
• Transport and scheduling: the most common trip length or arrival minute.
• Quality control: the most frequent defect count per batch.
• Grouped data: the modal class, meaning the interval with the highest frequency in a histogram.