5. (a) Explain briefly the advantages and disadvantages of using the quartiles to summarise a set of data.
(b) Describe the main features and uses of a box plot.
The distances, in kilometres, travelled to school by the teachers in two schools, \(A\) and \(B\), in the same town were recorded. The data for School \(A\) are summarised in Diagram 1.
\section*{Diagram 1}
\includegraphics[max width=\textwidth, alt={}]{516911a4-d55e-4008-bad5-7c97bea94f9f-4_540_1244_772_390}
For School \(B\), the least distance travelled was 3 km and the longest distance travelled was 55 km . The three quartiles were 17, 24 and 31 respectively.
An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.
(c) Draw a box plot for School B.
(d) Compare and contrast the two box plots.
(4)