What Is the Difference Between Mean, Median, and Mode?
Understand the difference between mean, median, and mode with simple examples, and learn when each type of average is the most honest description of data.
Three Ways to Describe the Middle of a Group
Mean, median, and mode are three different ways to describe what is typical or central in a set of numbers. Each one tells you something slightly different, and choosing the wrong one can give a misleading picture of the data.
Imagine a small town where five people earn $30,000, $35,000, $40,000, $45,000, and $1,000,000 per year. The mean (average) income is $230,000. The median income is $40,000. The mode is each number exactly once, so there is no mode. The mean gives a wildly different picture of typical income than the median because one outlier pulls it up dramatically.
This is why statisticians and analysts choose their measure of central tendency carefully based on the data and what they want to communicate. Understanding the difference helps you read statistics more critically.
Mean: The Average Everyone Knows
The mean is what most people call the average. To calculate it, add all the numbers together and divide by how many numbers there are. Five test scores of 72, 85, 90, 68, and 95 have a mean of (72 plus 85 plus 90 plus 68 plus 95) divided by 5, which equals 410 divided by 5, which equals 82.
The mean is useful when the data is fairly uniform and does not have extreme outliers. Grade point averages, batting averages in baseball, and temperature averages all use the mean appropriately because the underlying data tends to be distributed without extreme outliers.
The mean is sensitive to outliers, which is its biggest weakness. One very large or very small number can pull the mean significantly away from what most of the data looks like. This is why income statistics often report the median rather than the mean — a few billionaires dramatically raise the mean without affecting what most people actually earn.
Median: The True Middle Value
The median is the middle value when all numbers are arranged from smallest to largest. For an odd count of numbers, it is the exact middle number. For an even count, it is the average of the two middle numbers.
Using the five test scores above arranged in order: 68, 72, 85, 90, 95. The middle value is 85. So the median is 85. The mean was 82. They are close in this case because the data is fairly uniform.
The median is resistant to outliers. In the income example, the $1,000,000 earner does not change the median at all — it is still the middle value of the sorted list. This makes the median a better representation of typical income in a skewed distribution. Real estate prices, household incomes, and age distributions are often reported using medians for this reason.
Mode: The Most Common Value and When It Matters
The mode is the value that appears most often in a data set. For the test scores 68, 72, 85, 90, 95, there is no mode because each value appears exactly once. But for scores 72, 85, 72, 90, 85, 72, the mode is 72 because it appears three times.
A data set can have no mode, one mode, or multiple modes. When two values appear equally often, the set is bimodal. The mode is the only measure of central tendency that makes sense for categorical data — for example, the most common shoe size sold at a store, or the most frequently chosen answer on a survey.
The mode is less commonly used in statistical analysis than mean or median, but it is invaluable in specific contexts. A clothing manufacturer needs to know the most common size (mode) to know how much of each size to produce. A mode of 10 tells you what to stock most, regardless of what the mean or median size calculation says.