| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.8 This is a straightforward computational question requiring the standard PMCC formula with given data. While tedious with 10 data points, it involves only routine substitution into a formula with no conceptual difficulty or interpretation challenges beyond basic correlation understanding. The calculation is mechanical and well below average A-level difficulty. |
| Spec | 2.05f Pearson correlation coefficient5.08a Pearson correlation: calculate pmcc |
| Length | 24 | 25 | 19 | 28 | 27 | 21 | 35 | 23 | 32 | 26 |
| Maximum diameter | 18 | 14 | 16 | 11 | 13 | 14 | 12 | 16 | 15 | 14 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(r = -0.526\) to \(-0.525\) | B3 | AWFW |
| \(r = -0.53\) to \(-0.52\) | (B2) | AWFW; ignore sign |
| \(r = -0.6\) to \(-0.4\) | (B1) | AWFW; ignore sign |
| Attempt at \(\sum x\), \(\sum x^2\), \(\sum y\), \(\sum y^2\) and \(\sum xy\) OR attempt at \(S_{xx}\), \(S_{yy}\) and \(S_{xy}\) | (M1) | Values: 260, 6970, 143, 2083 and 3671; OR 210, 38.1 and \(-47\) |
| Attempt at correct formula for \(r\) | (m1) | |
| \(r = -0.526\) to \(-0.525\) | (A1) | 3; AWFW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Weak/some/moderate negative correlation (relationship/association) | B1 | OE; must qualify strength and indicate negative. B0 for strong/poor/reasonable/average. B0 if \(r>0\) or \(r<-1\). B0 if contradictory statements |
| between length and (maximum) diameter | B1 | Context |
| OR: Some evidence that large lengths are associated with small diameters | (B1)(B1) | OE; must qualify strength and indicate negative |
| OR: Longer melons tend to have smaller diameters / be thinner | (B1)(B1) | 2; OE; must qualify strength and indicate negative |
## Question 1:
**Part (a):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $r = -0.526$ to $-0.525$ | B3 | AWFW |
| $r = -0.53$ to $-0.52$ | (B2) | AWFW; ignore sign |
| $r = -0.6$ to $-0.4$ | (B1) | AWFW; ignore sign |
| Attempt at $\sum x$, $\sum x^2$, $\sum y$, $\sum y^2$ and $\sum xy$ OR attempt at $S_{xx}$, $S_{yy}$ and $S_{xy}$ | (M1) | Values: 260, 6970, 143, 2083 and 3671; OR 210, 38.1 and $-47$ |
| Attempt at correct formula for $r$ | (m1) | |
| $r = -0.526$ to $-0.525$ | (A1) | 3; AWFW |
**Part (b):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| Weak/some/moderate negative correlation (relationship/association) | B1 | OE; must qualify strength and indicate negative. B0 for strong/poor/reasonable/average. B0 if $r>0$ or $r<-1$. B0 if contradictory statements |
| between length and (maximum) diameter | B1 | Context |
| OR: Some evidence that large lengths are associated with small diameters | (B1)(B1) | OE; must qualify strength and indicate negative |
| OR: Longer melons tend to have smaller diameters / be thinner | (B1)(B1) | 2; OE; must qualify strength and indicate negative |
---1 The table shows the length, in centimetres, and maximum diameter, in centimetres, of each of 10 honeydew melons selected at random from those on display at a market stall.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Length & 24 & 25 & 19 & 28 & 27 & 21 & 35 & 23 & 32 & 26 \\
\hline
Maximum diameter & 18 & 14 & 16 & 11 & 13 & 14 & 12 & 16 & 15 & 14 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the product moment correlation coefficient.
\item Interpret your value in the context of this question.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2007 Q1 [5]}}