Mean, Median and Mode Explained (With Examples)

"Average" is one of the most misused words in everyday math, because there are actually three common averages — the mean, the median and the mode — and they can tell very different stories about the same data. Knowing which one to use is often more important than the calculation itself. You can compute all three at once with our mean calculator.

The mean (arithmetic average)

The mean is what most people picture: add up all the values and divide by how many there are.

mean = sum of values ÷ number of values

For the data set 12, 15, 20, 22, 31:

1. Sum: 12 + 15 + 20 + 22 + 31 = 100
2. Count: 5
3. Mean: 100 ÷ 5 = 20

The mean uses every value, which makes it powerful — but also sensitive to extremes.

The median (the middle value)

The median is the middle value when the data is sorted from smallest to largest. With an odd number of values, it's the single middle one. With an even number, it's the average of the two middle values.

For 4, 8, 15, 16 (already sorted), the two middle values are 8 and 15, so:

median = (8 + 15) ÷ 2 = 11.5

The median ignores how extreme the outer values are — it only cares about position. That property makes it invaluable, as we'll see.

The mode (the most common value)

The mode is simply the value that appears most often. In 3, 7, 7, 7, 9, 12, the mode is 7. Data can have one mode, several modes, or none at all if every value is unique. The mode is the only average that works for non-numeric (categorical) data — like the most common shoe size sold.

Why the choice matters: outliers

Here's where it gets practical. Imagine five households with these annual incomes (in thousands):

30, 32, 35, 38, 500

• The mean is (30 + 32 + 35 + 38 + 500) ÷ 5 = 127.
• The median is 35.

The mean of 127 suggests a comfortable middle income — but four of the five households earn under 40. That single high earner (an outlier) has dragged the mean far from what's typical. The median of 35 describes the group much more honestly.

This is exactly why economists report median income and house prices rather than the mean: skewed data with a long tail makes the mean misleading.

A quick decision guide

• Symmetric data, no big outliers? The mean is usually best — it uses all the information.
• Skewed data or outliers? Prefer the median.
• Categorical data, or you want the "most popular" value? Use the mode.

Don't forget the spread

Averages only tell you the centre of your data, not how spread out it is. Two classes can both average 70% on a test while one has everyone near 70 and the other has a mix of 40s and 90s. That's why statisticians pair an average with a measure of spread like the range or the standard deviation — both of which our mean calculator reports alongside the averages.

Try it yourself

Paste a list of numbers into the mean calculator and compare the mean and median. The bigger the gap between them, the more skewed your data is — and the more you should trust the median to describe what's typical.