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NEXUS

- EDEXCEL GCSE
- AQA GCSE
- OCR GCSE
- EDUQAS GCSE

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.

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.

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.

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.

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).

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

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