Learn how to calculate the mean, median, and mode of a set of numbers, and when each one gives a more accurate picture than the others.
“Average” usually means the mean — add everything up and divide by how many numbers there are — but it’s not the only way to describe a “typical” value in a set of numbers. Here’s how to calculate all three common types, and when each one gives a more honest picture than the others.
For the numbers 4, 8, 6, 5, 3: add them up (4 + 8 + 6 + 5 + 3 = 26), then divide by how many there are (5). The mean is 26 ÷ 5 = 5.2.
Sort the numbers from smallest to largest, then find the middle one. For an odd count, that’s a single middle number. For an even count, it’s the mean of the two middle numbers.
For 4, 8, 6, 5, 3 — sorted: 3, 4, 5, 6, 8 — the middle value is 5, so the median is 5.
For an even-count example, 4, 8, 6, 5 — sorted: 4, 5, 6, 8 — the two middle values are 5 and 6, so the median is (5 + 6) ÷ 2 = 5.5.
The mode is simply whichever value appears most often. In 4, 8, 6, 5, 3, 5, the number 5 appears twice while every other number appears once, so the mode is 5. A set can have no mode (nothing repeats), one mode, or several tied modes.
The mean is sensitive to extreme values (“outliers”). In the salaries 40k, 42k, 45k, 41k, and 400k, the mean is pulled up to 113.6k by the one very high value — a number that doesn’t represent any of the five salaries well. The median (42k) gives a far more typical picture of this particular data set.
Scores: 72, 85, 90, 85, 60.
Average Calculator
Add up all the values in the set, then divide that total by the number of values. This is technically called the mean, though it’s what most people mean by “average.”
The mean is the sum divided by the count. The median is the middle value once the numbers are sorted. The mode is whichever value appears most often. All three describe a “typical” value, but can give different answers for the same data set.
When a data set has extreme outliers that would otherwise skew the mean, the median usually gives a more representative “typical” value — household income and home prices are commonly reported as medians for exactly this reason.
Yes. If two or more values are tied for the most frequent, the set has multiple modes; if every value appears exactly once, there is no mode at all.
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