6 The table shows the total distance travelled, in thousands of miles, and the amount of commission earned, in thousands of pounds, by each of seven sales agents in 2005.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Agent & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
Distance travelled & 18 & 15 & 12 & 14 & 16 & 24 & 13 \\
\hline
Commission earned & 18 & 45 & 19 & 24 & 27 & 22 & 23 \\
\hline
\end{tabular}
\end{center}

(i) (a) Calculate Spearman's rank correlation coefficient, $r _ { s }$, for these data.\\
(b) Comment briefly on your value of $r _ { s }$ with reference to this context.\\
(c) After these data were collected, agent $A$ found that he had made a mistake. He had actually travelled 19000 miles in 2005. State, with a reason, but without further calculation, whether the value of Spearman's rank correlation coefficient will increase, decrease or stay the same.

The agents were asked to indicate their level of job satisfaction during 2005. A score of 0 represented no job satisfaction, and a score of 10 represented high job satisfaction. Their scores, $y$, together with the data for distance travelled, $x$, are illustrated in the scatter diagram below.\\
\begin{tikzpicture}[
    >=Stealth,
    x=0.6cm, 
    y=0.55cm
]

    % Grid lines (light) - drawn first so they remain behind the axes
    \foreach \x in {10,11,...,26} {
        \draw[gray!20, very thin] (\x, 0) -- (\x, 10.5);
    }
    \foreach \y in {0,1,...,10} {
        \draw[gray!20, very thin] (10, \y) -- (26.5, \y);
    }

    % Axes
    \draw[->, thick] (10, 0) -- (27.5, 0) node[right] {$x$};
    \draw[->, thick] (10, 0) -- (10, 11.5) node[above] {$y$};

    % X-axis tick marks and labels
    \foreach \x in {10, 15, 20, 25} {
        \draw[thick] (\x, 0) -- (\x, -0.2) node[below=2pt] {$\x$};
    }

    % Y-axis tick marks and labels
    \foreach \y in {0, 5, 10} {
        \draw[thick] (10, \y) -- (9.8, \y) node[left=2pt] {$\y$};
    }

    % Data points as crosses using standard TikZ plot marks
    \draw plot[only marks, mark=x, mark options={thick}, mark size=4pt] 
        coordinates {
            (12,10) 
            (13,7.5) 
            (14,6.5) 
            (15,5) 
            (16,4) 
            (21,2.5) 
            (24,1)
        };

\end{tikzpicture}\\
(ii) For this scatter diagram, what can you say about the value of\\
(a) Spearman's rank correlation coefficient,\\
(b) the product moment correlation coefficient?

\hfill \mbox{\textit{OCR S1 2006 Q6 [10]}}