2 Doug has a list of times taken by competitors in a 'fun run'. He has grouped the data and calculated the frequency densities in order to draw a histogram to represent the information. Some of the data are presented in Fig. 2.
\begin{table}[h]
| Time in minutes | \(15 -\) | \(20 -\) | \(25 -\) | \(35 -\) | \(45 - 60\) |
| Number of runners | 12 | 23 | 59 | 71 | |
| Frequency density | 2.4 | | 5.9 | 7.1 | 1.4 |
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{table}
- Write down the missing values in the copy of Fig. 2 in the Printed Answer Booklet.
- Doug labels the horizontal axis on the histogram 'time in minutes' and the vertical axis 'number of minutes per runner'. State which one of these labels is incorrect and write down a correct version.
\(3 \quad P\) and \(Q\) are consecutive odd positive integers such that \(P > Q\).
Prove that \(P ^ { 2 } - Q ^ { 2 }\) is a multiple of 8 .