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Averages: mean, median, mode and range

Years 6 to 11

Different ways to describe a typical value, and how spread out the data is.

The numbers 2, 3, 3, 5, 7, 8, 9. The mode is 3, the median is 5 and the mean is about 5.3.

For learners

An average tells you what is typical. There are three kinds.

The mode is the number that appears most often.
The median is the middle number when they are in order.
The mean is all the numbers added up, then divided by how many there are.

The range tells you how spread out the numbers are: the biggest number minus the smallest.

A worked example

Find the mean of 4, 6, 6, 8 and 11.

Add: $4 + 6 + 6 + 8 + 11 = 35$ .
There are 5 numbers.
$35 \div 5 = 7$ .

For grown-ups

Always put the numbers in order before finding the median. With an even number of values, the median is halfway between the two middle ones. The mean is affected by very large or small values, so the median is often a better 'typical' value for things like house prices.

Common mistakes

Finding the median without ordering the list first.
Dividing by the wrong number when finding the mean.
Giving the number that is most common as the mean.

Why it matters

News, sports, weather and science all use averages to make sense of a lot of numbers.

Topics in quarter that use this

Averages and range
Averages from tables
Cumulative frequency and box plots
The normal distribution