Averages and Range

An average is a value used to summarise a data set with a single number representing its central tendency. There are three main types of averages; the mean, median and mode.

Mean

The sum of all values divided by the number of values.

\[\text{mean} = \frac{\sum x}{n}\]

\(\sum x\) is the sum of all data points and \(n\) is the number of data points.

Median

The middle value of a data set when the values are arranged in ascending order. If there is an even number of values, the median is the average of the two middle numbers.

Mode

The value that appears most frequently in a data set. There can be more than one mode, or no mode if all values are unique.

Range

The range is not an average, but measures the spread of the data by subtracting the smallest value from the largest value:

\[\text{Range} = \text{Maximum} - \text{Minimum}\]

It gives a simple measure of how spread out the values are but can be affected by extreme values (outliers).

Grouped data

When the data is grouped, you must use the midpoints of each group to represent all the data in the group.