| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 4 |
| 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 calculation question requiring direct substitution into the PMCC formula r = S_xy/√(S_xx × S_yy). All summary statistics are provided, so it requires only recall of the formula and careful calculator work. No interpretation complexity or problem-solving is needed for part (a), and part (b) is routine contextual interpretation. |
| Spec | 5.08a Pearson correlation: calculate pmcc |
| \(\boldsymbol { x }\) | 21371 | 18521 | 15222 | 17312 | 19854 | 23561 | 20738 | 22111 | 17897 | 24523 |
| \(\boldsymbol { y }\) | 2281 | 2327 | 2221 | 2378 | 2787 | 2856 | 3078 | 2647 | 2566 | 2559 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(r_{xy} = \dfrac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}}\) | M1 | Correct formula used with given values substituted |
| \(r_{xy} = \dfrac{3629670}{\sqrt{76581640 \times 694250}}\) | ||
| \(r_{xy} = \dfrac{3629670}{\sqrt{53162552050000}}\) | ||
| \(r_{xy} = \dfrac{3629670}{7291265...} = 0.4977... \approx 0.498\) | A1 | Accept awrt \(0.498\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| There is a weak/moderate positive (linear) correlation between annual gas consumption and annual electricity consumption (for bungalows of similar size and occupancy) | B1 | Must mention positive and weak/moderate in context |
| As gas consumption increases, electricity consumption also tends to increase | B1 | Context required for second mark |
# Question 1:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $r_{xy} = \dfrac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}}$ | M1 | Correct formula used with given values substituted |
| $r_{xy} = \dfrac{3629670}{\sqrt{76581640 \times 694250}}$ | | |
| $r_{xy} = \dfrac{3629670}{\sqrt{53162552050000}}$ | | |
| $r_{xy} = \dfrac{3629670}{7291265...} = 0.4977... \approx 0.498$ | A1 | Accept awrt $0.498$ |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| There is a weak/moderate positive (linear) correlation between annual gas consumption and annual electricity consumption (for bungalows of similar size and occupancy) | B1 | Must mention positive and weak/moderate in context |
| As gas consumption increases, electricity consumption also tends to increase | B1 | Context required for second mark |
---1\\
The table shows the annual gas consumption, $x \mathrm { kWh }$, and the annual electricity consumption, $y \mathrm { kWh }$, for a sample of 10 bungalows of similar size and occupancy.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 21371 & 18521 & 15222 & 17312 & 19854 & 23561 & 20738 & 22111 & 17897 & 24523 \\
\hline
$\boldsymbol { y }$ & 2281 & 2327 & 2221 & 2378 & 2787 & 2856 & 3078 & 2647 & 2566 & 2559 \\
\hline
\end{tabular}
\end{center}
$$S _ { x x } = 76581640 \quad S _ { y y } = 694250 \quad S _ { x y } = 3629670$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of $r _ { x y }$, the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value of $r _ { x y }$ in the context of this question.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2015 Q1 [4]}}