3 A sample of bivariate data was taken and the results were summarised as follows.

$$n = 5 \quad \Sigma x = 24 \quad \Sigma x ^ { 2 } = 130 \quad \Sigma y = 39 \quad \Sigma y ^ { 2 } = 361 \quad \Sigma x y = 212$$
\begin{enumerate}[label=(\roman*)]
\item Show that the value of the product moment correlation coefficient $r$ is 0.855 , correct to 3 significant figures.
\item The ranks of the data were found. One student calculated Spearman's rank correlation coefficient $r _ { s }$, and found that $r _ { s } = 0.7$. Another student calculated the product moment coefficient, $R$, of these ranks. State which one of the following statements is true, and explain your answer briefly.\\
(A) $R = 0.855$\\
(B) $R = 0.7$\\
(C) It is impossible to give the value of $R$ without carrying out a calculation using the original data.
\item All the values of $x$ are now multiplied by a scaling factor of 2 . State the new values of $r$ and $r _ { s }$.
\end{enumerate}

\hfill \mbox{\textit{OCR S1 2008 Q3 [6]}}