24.3 Averages and range — Learn

Prerequisites: ordering numbers and dividing exactly or approximately.

Objectives: calculate and interpret mean, median, mode and range; compare what each measure describes.

The mean is total divided by count. The median is the middle value after ordering. The mode is the most frequent value. The range is maximum minus minimum. These are measures of a data set; an unusual value, called an outlier, can affect the mean and range strongly.

Example. Find the mean, median, mode and range of $3, 4, 4, 7, 12$.

Add the values: $3+4+4+7+12=30$.

Divide by five: mean $=30/5=6$.

The ordered middle value is 4, so median $=4$.

The most frequent value is 4, so mode $=4$.

Subtract the extremes: range $=12-3=9$.

Example. Compare the mean and median after adding 30 to the list.

The new total is $30+30=60$ for six values.

The new mean is $60/6=10$.

The middle pair is 4 and 7, so median $=(4+7)/2=5.5$.

The large value raises the mean more than the median.

Watch out. The median is not always one of the data values. With an even count, average the two middle values.

Progress check

Which average would you report for the number of pupils choosing each travel method? Explain why the mode could help.

You should now be able to

• calculate mean, median, mode and range;
• describe how an outlier can affect a measure;
• compare data sets using suitable measures.