5 As part of a study of charity shops in a small market town, two such shops, \(X\) and \(Y\), were each asked to provide details of its takings on 12 randomly selected days. The table shows, for each of the 12 days, the day's takings, \(\pounds x\), of charity shop \(X\) and the day's takings, \(\pounds y\), of charity shop \(Y\).

1. 1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
   2. Interpret your value in the context of this question.
2. Complete the scatter diagram shown on the opposite page.
3. The investigator realised subsequently that one of the 12 selected days was a particularly popular town market day and another was a day on which the weather was extremely severe. Identify each of these days giving a reason for each choice.
4. Removing the two days described in part (c) from the data gives the following information. $$S _ { x x } = 1292.5 \quad S _ { y y } = 3850.1 \quad S _ { x y } = 407.5$$
   1. Use this information to recalculate the value of the product moment correlation coefficient between \(x\) and \(y\).
   2. Hence revise, as necessary, your interpretation in part (a)(ii).
      [0pt] [3 marks] Shop \(X\) takings（£） \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{harity Shops} \includegraphics[alt={},max width=\textwidth]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_33_21_294_1617}
      \end{figure} \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{harity Shops} \includegraphics[alt={},max width=\textwidth]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_49_24_276_1710}
      \end{figure}
      \includegraphics[max width=\textwidth, alt={}]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_1304_415_406_1391}
      レ