Content description

Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

There are a number of ways of measuring the location (centre) of a data set. The three most common are the mean, the median and the mode.

Mean

The mean of a data set is one measure of its centre. It is calculated by first adding together all the data values and then dividing the sum by the number of data values.

This formula can be used:

\(\text{Mean}\ =\ \dfrac{\text{sum of values}}{\text{number of values}}\)

The most common name for mean is 'average'.

Example 1

Michael obtained the following marks in eight tests:

43

35

41

29

33

39

47

42

Calculate the mean.

Solution

\begin{align}\text{Mean}\ &=\ \dfrac{\text{sum of values}}{\text{number of values}}\\\\ &=\ \dfrac{43 + 35 + 41 + 29 + 33 + 39 + 47 + 42}{8}\\\\ &=\ \dfrac{309}{8}\\\\ &= 38.625\end{align}

Note that the mean was not a mark obtained by Michael in any of his tests.