What Are Mean, Median, Mode and Range?
Mean, median and mode are three ways of answering the same question: what is a typical value in this dataset? They usually give similar answers, and they disagree exactly when the data is interesting.
The mean
Add every value together and divide by how many values there are. The mean uses every value, which makes it a fair average when the data is fairly even, and a misleading one when a single extreme value sits far from the rest.
x̄ = Σx ÷ n
The median
Put the values in order and take the middle one. An odd count gives one middle value; an even count gives two, and their average is the median. Because it depends on position rather than size, the median barely moves when an extreme value is added.
The mode
The value that appears most often. Two tied values make the dataset bimodal, three or more make it multimodal, and if nothing repeats there is no mode. The mode is the only one of the three that works for categories such as colors or shoe sizes.
A dataset where all three give a different answer
Take the values 5, 6, 7, 8, 100.
- The sum is 126 and there are five values, so the mean is 126 ÷ 5 = 25.2.
- Sorted, the middle value is 7, so the median is 7.
- Every value appears once, so there is no mode.
The mean of 25.2 does not describe any of the values, because the 100 has pulled it upwards. The median of 7 describes the dataset honestly. This one example is the reason the median is reported alongside the mean for salaries, house prices and waiting times.
A dataset where all three agree
For 4, 5, 5, 5, 6 the mean is 25 ÷ 5 = 5, the median is 5 and the mode is 5. Here the three measures agree because the data is centered around 5 without an extreme value pulling the mean away from the middle.
What are mean, median, mode and range?
Mean, median, mode and range are four simple ways to describe a list of numbers.
- Mean: the average. Add all the numbers, then divide by how many numbers there are.
- Median: the middle number when the numbers are in order.
- Mode: the number that appears most often.
- Range: the biggest number minus the smallest number. It shows how spread out the numbers are.
How do you find the mean, median, mode and range?
Try this list: 5, 10, 3, 5, 7.
- Put the numbers in order: 3, 5, 5, 7, 10.
- Mean: add them up, 3 + 5 + 5 + 7 + 10 = 30. Then divide by how many numbers there are (5). 30 ÷ 5 = 6.
- Median: the middle number in the ordered list is 5.
- Mode: the number that shows up most often. The number 5 appears twice, so the mode is 5.
- Range: the biggest number minus the smallest number. 10 − 3 = 7.
So the mean is 6, the median is 5, the mode is 5 and the range is 7.
Is the mean the same as the average?
Yes. In school math, the mean is the average: add the numbers and divide by how many there are. Some people also use the word average for the median or the mode, so the word mean is the clearest choice when you want to be exact.
Does the order matter: mean mode median or median mode mean?
No. You may see the words written as mean, median, mode, or mean, mode, median, or median, mode, mean. They are the same three measures, and the order does not change any answer. Add “and range” and you have the four measures most school lessons teach.
Is there a free mean, median, mode and range worksheet?
Yes. The Practice Questions page has questions with answers and a free worksheet PDF that you can download and print.
Want to check your own numbers? Use the mean, median, mode and range calculator, or open the range calculator.