| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Easy -1.2 This is a routine computational question requiring students to apply the PMCC formula to given data - a standard textbook exercise with no conceptual challenges. Part (b) tests basic understanding that correlation is scale-invariant, which is straightforward recall. The calculation is tedious but mechanical, typical of easier S1 questions. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc |
| Time (x) | 13 | 4 | 5 | 10 | 9 | 17 | 23 | 16 | 2 | 16 |
| Value (y) | 12.5 | 5.7 | 2.3 | 18.4 | 7.9 | 17.1 | 17.9 | 18.6 | 8.3 | 21.3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(r = 0.797\) | B3 | AWRT |
| \(r = 0.79\) to \(0.81\) | (B2) | AWFW; accept 0.80 but not 0.8 |
| \(r = 0.8\) | (B1) | |
| Attempt at \(\Sigma x\), \(\Sigma x^2\), \(\Sigma y\), \(\Sigma y^2\), \(\Sigma xy\) OR attempt at \(S_{xx}\), \(S_{yy}\), \(S_{xy}\) | (M1) | 115, 1725; 130, 2076.36; 1809.3 OR 402.5; 386.36; 314.3 |
| Attempt at a correct formula for \(r\) | (m1) | |
| \(r = 0.797\) | (A1) | AWRT |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Strong (fairly strong) evidence of a positive (direct) linear correlation (association/relationship) | B1 | Not 'some' or 'weak' or 'good'; must use 'positive' or equivalent and 'correlation' or equivalent; accept 'high' as alternative to 'strong' |
| between time in store and value of items purchased | B1 | Context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(r =\) Answer to (a)(i) OR \(0.797\) | B1\(\sqrt{}\) | \(\sqrt{}\) on (a)(i) providing \(-1 < r < 1\); AWRT |
# Question 1:
## Part (a)(i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $r = 0.797$ | B3 | AWRT |
| $r = 0.79$ to $0.81$ | (B2) | AWFW; accept 0.80 but not 0.8 |
| $r = 0.8$ | (B1) | |
| Attempt at $\Sigma x$, $\Sigma x^2$, $\Sigma y$, $\Sigma y^2$, $\Sigma xy$ OR attempt at $S_{xx}$, $S_{yy}$, $S_{xy}$ | (M1) | 115, 1725; 130, 2076.36; 1809.3 OR 402.5; 386.36; 314.3 |
| Attempt at a correct formula for $r$ | (m1) | |
| $r = 0.797$ | (A1) | AWRT |
## Part (a)(ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| **Strong** (fairly strong) evidence of a **positive** (direct) linear **correlation** (association/relationship) | B1 | Not 'some' or 'weak' or 'good'; must use 'positive' or equivalent and 'correlation' or equivalent; accept 'high' as alternative to 'strong' |
| between **time in store** and **value of items purchased** | B1 | Context |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $r =$ Answer to (a)(i) OR $0.797$ | B1$\sqrt{}$ | $\sqrt{}$ on (a)(i) providing $-1 < r < 1$; AWRT |
---1 For each of a random sample of 10 customers, a store records the time, $x$ minutes, spent shopping and the value, $\pounds y$, to the nearest 10 p, of items purchased. The results are tabulated below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Time (x) & 13 & 4 & 5 & 10 & 9 & 17 & 23 & 16 & 2 & 16 \\
\hline
Value (y) & 12.5 & 5.7 & 2.3 & 18.4 & 7.9 & 17.1 & 17.9 & 18.6 & 8.3 & 21.3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the value of the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value in context.
\end{enumerate}\item Write down the value of the product moment correlation coefficient if the time had been recorded in seconds and the value in pence to the nearest 10p.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2005 Q1 [6]}}