5 [Figure 1, printed on the insert, is provided for use in this question.]\\
The table shows the times, in seconds, taken by a random sample of 10 boys from a junior swimming club to swim 50 metres freestyle and 50 metres backstroke.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Boy & A & B & C & D & E & F & G & H & I & J \\
\hline
Freestyle ( $\boldsymbol { x }$ seconds) & 30.2 & 32.8 & 25.1 & 31.8 & 31.2 & 35.6 & 32.4 & 38.0 & 36.1 & 34.1 \\
\hline
Backstroke ( $y$ seconds) & 33.5 & 35.4 & 37.4 & 27.2 & 34.7 & 38.2 & 37.7 & 41.4 & 42.3 & 38.4 \\
\hline
\end{tabular}
\end{center}

(a) On Figure 1, complete the scatter diagram for these data.\\
(b) Hence:\\
(i) give two distinct comments on what your scatter diagram reveals;\\
(ii) state, without calculation, which of the following 3 values is most likely to be the value of the product moment correlation coefficient for the data in your scatter diagram.

$$0.912 \quad 0.088 \quad 0.462$$

(c) In the sample of 10 boys, one boy is a junior-champion freestyle swimmer and one boy is a junior-champion backstroke swimmer.

Identify the two most likely boys.\\
(d) Removing the data for the two boys whom you identified in part (c):\\
(i) calculate the value of the product moment correlation coefficient for the remaining 8 pairs of values of $x$ and $y$;\\
(ii) comment, in context, on the value that you obtain.

\hfill \mbox{\textit{AQA S1  Q5}}