Mean, median, mode and range

In a nutshell

An average is a common or typical value. In statistics, there are three different types of averages that can be measured from a dataset: the mean, median and mode. The range of a dataset is the lowest value subtracted from the highest value.

The mean

To calculate the mean of a dataset, add up all the values in the dataset and then divide by how many items there are.

Example 1

A group of students take a maths test and obtain the scores below. What is the mean score?

$$13, 7, 15, 6, 8$$​​

Add the scores up and divide by the number of items:

$$\begin{aligned}mean& = \dfrac{13+7+15+6+8}{5} \\mean &= 9.8\end{aligned}$$​​

Therefore, the mean score is $$\underline{9.8}$$.​

The median

The median is the middle value after all the numbers in the dataset have been arranged in order from smallest to largest.

Example 2

Find the median of the following dataset:

$$7, 15, 21, 3, 10, 9, 13$$​​

First write the numbers in ascending order:

$$3, 7, 9, 10, 13, 15, 21$$​​

The median number is the value where there is an equal amount of numbers either side. In this case, $$10$$ has three numbers either side of it.

Therefore, the median is $$\underline{10}$$.

The mode

The mode is the most common value that appears in the dataset.

Example 3

Some students enter a singing competition, their ages are shown below. What is the mode?

$$11, 9, 7 ,11, 10, 10, 11, 8, 9, 11$$​​

The number $$11$$ comes up most often.

Therefore, the mode is $$\underline{11}$$.

The range

The range is the difference between the largest value and the smallest value in the dataset.

Example 4

Ten students in year six run a race. Their times, recorded to the nearest second, are given below. What is the range?

$$13, 11, 25, 13, 14, 15, 12,21, 18, 16$$​​

Find the highest value and the lowest value and subtract them to find the range.

$$\begin{aligned}range &= highest - lowest \\range &= 25-11 \\range &=14\end{aligned}$$​​

Therefore, the range is $$\underline{14}$$.