Mean, Median, and Mode: What's the Difference?
All three are called the average and they measure different things. The Average / Median Calculator gives all of them, plus the range, which is usually the fastest way to see whether they disagree.
What each one is
The mean adds everything and divides by the count. It uses every value, which makes it sensitive to extremes.
The median is the middle value when the numbers are sorted - or the average of the middle two if there is an even count. It ignores how far out the extremes are.
The mode is the most frequent value. It is the only one that works on data that is not numeric at all, which is why it is the average for things like favourite colour.
When they disagree, and why it matters
Take seven salaries: 22, 24, 25, 26, 28, 30 and 450 thousand.
The mean is 86. The median is 26. One person's salary has pulled the mean to more than three times what six of the seven people earn, and the mean is not wrong - it is just answering a question nobody asked.
This is exactly why income and house prices are reported as medians. A single large value drags a mean a long way and leaves a median untouched, and for skewed data the median describes a typical case far better.
The practical test: if the mean and the median are far apart, the data is skewed, and the median is probably the honest number. The Standard Deviation Calculator tells you how spread out it is as well.
Where each one belongs
Mean for symmetrical data with no extreme outliers, and whenever you need a total - the mean times the count gives the sum back, which neither of the others does. Exam marks, measurement averages, rainfall.
Median for income, house prices, response times, waiting times - anything with a long tail. Also for small data sets where one bad reading would distort the mean.
Mode for categories, for the most common size or model, and for genuinely multi-peaked data where a single average is misleading anyway.
The honest warning
Someone quoting "the average" without saying which has told you less than they appear to, and the choice between them can be made to flatter. A company's average salary looks very different depending on which one you pick, and both figures can be published truthfully.
So when you read an average, ask which. When you publish one, say which.
Common questions
Can there be more than one mode?
Yes - two or more values can tie. A data set with two peaks is bimodal, which usually means two different groups are mixed together.
What if there is no repeated value?
Then there is no mode, which is common in continuous measurements.
What is the range?
The largest value minus the smallest. Crude, instant, and a useful first look at spread.
Which average do exam grades use?
The mean, usually, because totals matter. A median would ignore how far above or below the middle each mark sat.
Got some numbers to summarise?