| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.3 This is a standard S1 correlation calculation requiring the PMCC formula with given data (9 values), followed by routine interpretation. Part (b) requires recognizing an implausible negative correlation between length and weight. While computational, it's slightly easier than average due to being a textbook application with no conceptual surprises, though the arithmetic with 9 data points prevents it from being trivial. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc |
| \(\boldsymbol { x }\) | 16.2 | 13.1 | 10.4 | 12.1 | 14.6 | 9.7 | 11.8 | 13.6 | 17.3 |
| \(\boldsymbol { y }\) | 4.2 | 3.9 | 4.7 | 3.3 | 3.7 | 2.4 | 3.1 | 3.5 | 2.7 |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = 0.022\) to \(0.023\) | B3 | AWFW (0.0225557) |
| \(r = 0.02\) to \(0.03\) | B2 | AWFW |
| \(r = -0.1\) to \(0.1\) | B1 | AWFW |
| OR Attempt at \(\sum x\), \(\sum x^2\), \(\sum y\), \(\sum y^2\) & \(\sum xy\) or Attempt at \(S_{xx}\), \(S_{yy}\) & \(S_{xy}\) | M1 | 118.8, 1619.36, 31.5, 114.43 & 416.13 (all 5 attempted) or 51.2, 4.18 & 0.33 (all 3 attempted) |
| Attempt at correct formula for \(r\) \(r = 0.022\) to \(0.023\) | m1 (A1) | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| (Almost/virtually) no/zero (linear) correlation (relationship/association/link) between length and (maximum) diameter of carrots | B1 | |
| B1 | 2 | Context; providing \(-1 < r < 1\) |
| Unlikely/wrong/incorrect/invalid Would expect a positive value or Would expect weight to increase with length or Would imply shorter carrots are heavier | B1 | |
| 2 |
**2(a)(i)**
| $r = 0.022$ to $0.023$ | B3 | AWFW (0.0225557) |
| $r = 0.02$ to $0.03$ | B2 | AWFW |
| $r = -0.1$ to $0.1$ | B1 | AWFW |
| OR Attempt at $\sum x$, $\sum x^2$, $\sum y$, $\sum y^2$ & $\sum xy$ or Attempt at $S_{xx}$, $S_{yy}$ & $S_{xy}$ | M1 | 118.8, 1619.36, 31.5, 114.43 & 416.13 (all 5 attempted) or 51.2, 4.18 & 0.33 (all 3 attempted) |
| Attempt at correct formula for $r$ $r = 0.022$ to $0.023$ | m1 (A1) | 3 | AWFW or equivalent qualification of NO strength; do not follow-through from (i); B0 for very weak/weak/some/little/slight/positive/hardly any/etc unless correct qualification also stated |
**2(a)(ii)**
| (Almost/virtually) **no/zero** (linear) **correlation** (relationship/association/link) between length and (maximum) diameter of carrots | B1 | |
| | B1 | 2 | Context; providing $-1 < r < 1$ |
| **Unlikely/wrong/incorrect/invalid** Would expect a **positive value** or Would expect **weight to increase with length** or Would imply **shorter carrots are heavier** | B1 | | Or equivalent |
| | | 2 | |
**Total for Q2: 7 marks**
---2 A greengrocer sells bunches of 9 carrots at his Saturday market stall. Tom and Geri are two Statistics students who work on the stall. Each selects a bunch of carrots at random.
\begin{enumerate}[label=(\alph*)]
\item At home, Tom measures the length, $x$ centimetres, and the maximum diameter, $y$ centimetres, of each carrot in his selected bunch with the following results.
\begin{center}
\begin{tabular}{ | r | r | r | r | r | r | r | r | r | r | }
\hline
$\boldsymbol { x }$ & 16.2 & 13.1 & 10.4 & 12.1 & 14.6 & 9.7 & 11.8 & 13.6 & 17.3 \\
\hline
$\boldsymbol { y }$ & 4.2 & 3.9 & 4.7 & 3.3 & 3.7 & 2.4 & 3.1 & 3.5 & 2.7 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Calculate the value of the product moment correlation coefficient.
\item Interpret your value in context.
\end{enumerate}\item At her home, Geri measures the length, in centimetres, and the weight, in grams, of each carrot in her selected bunch and then obtains a value of - 0.986 for the product moment correlation coefficient.
Comment, with a reason, on the likely validity of Geri's value.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2009 Q2 [7]}}