Mean, median and mode: which average to use

Mean, median and mode are all called averages, and each one answers the question "what is typical?" in its own way. The mean adds up every value and divides by how many there are. The median is the middle value once the numbers are sorted from smallest to largest. The mode is the value that occurs most often. For a set of numbers that is roughly even, the three tend to land close together, which is why they are often used interchangeably. When the values are spread out or lopsided, they can disagree sharply, and choosing the right one matters.

Take a small made-up example. Seven people report how many books they read last month: 0, 1, 1, 2, 3, 3 and 12. The mean is 22 divided by 7, which is about 3.1. The median is 2, because the fourth value in the sorted list is the middle one. The mode is both 1 and 3, since each appears twice. The one reader who finished 12 books pulls the mean well above the median, while the mode points to two different typical answers. The same data produce three different summaries.

Calculating each average with care

To calculate the mean, add the values and divide by the count. Two errors are common: dividing by the wrong count, such as the number of non-zero entries, and averaging group means without weighting each group by its size. Suppose one support team resolves 10 tickets in an average of 4 hours and another resolves 90 tickets in an average of 12 hours. Averaging the two team means gives 8 hours, but the true average across all 100 tickets is 11.2 hours. The median takes a sorting step first. With an odd count, the median is the middle value. With an even count, average the two middle values, so that a set of six values has a median equal to the average of the third and fourth.

Writing the sorted values in a column, one per line, is the simplest way to avoid one of the most common median mistakes, which is picking the middle of the list before it has been sorted.

The mode needs no arithmetic, only counting. It is the most frequent value. A set can have one mode, several modes when values tie for the highest count, or none at all when every value appears only once. Because the mode does not depend on order or on the size of the values, it is the only one of the three that works for categories with no natural order, such as colors, brands or answers to a yes-or-no question.

Use the mean when totals matter

The mean is the right tool when totals matter, because multiplying it by the count recovers the sum. It also responds to every value: in a set of seven values, changing one value by 10 units moves the mean by 10 divided by 7, about 1.4 units. The median stays put so long as the changed value remains on the same side of the middle and is not the middle value itself, which is one reason the two averages can tell different stories.

Choose the median or mode for ratings and categories

Ratings on a 1-to-5 satisfaction scale have an order, but the steps between them are not guaranteed to be equal, because nothing says the gap from neutral to satisfied matches the gap from satisfied to very satisfied. The median uses only the order, so it is the more defensible summary of a typical response. Suppose nine people answer 1, 2, 3, 3, 4, 4, 4, 5 and 5. The median and the mode are both 4, while the mean is about 3.4, a figure that quietly assumes the steps are equal.

The mode suits data where repeated values carry meaning, such as the most common shoe size sold in a store or the most frequent answer to a survey with fixed options. It can mislead when the values are nearly all different, because the most frequent one may appear only twice and say little about the rest.

Suppose 50 people name their favorite of four colors, and the counts are 18 for blue, 14 for green, 12 for red and 6 for yellow. The mode is blue. A mean cannot be calculated for colors, because they are not numbers, and a median has no meaningful middle position when the categories have no order. Here the mode is the only average that answers the question the survey asked.

Match the average to the question

The three averages answer slightly different questions, so the table below is a quick guide to choosing among them.

Scroll sideways to see the full table →

When a report says only "the average," look for the footnote that names it, because the mean and median of the same data can differ a great deal. Whichever average you use, state its name beside the figure, so that a reader can check it without guessing.