| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of the PMCC formula using given summary statistics. Students need only substitute values into a standard formula (no derivation required) and perform arithmetic calculations. The context interpretation in part (c) is minimal. This is easier than average as it's pure formula recall with no problem-solving or conceptual challenges. |
| Spec | 2.02c Scatter diagrams and regression lines2.05f Pearson correlation coefficient |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Scatter diagram with points plotted | B3 | |
| (b) \(S_{YY} = 140 - \frac{28^2}{8} = 42\) | M1 | |
| \(S_{YY} = 4173.93 - \frac{182.5^2}{8} = 10.64875\) | M1 | |
| \(S_{YY} = 644.7 - \frac{28 \times 182.5}{8} = 5.95\) | M1 | |
| \(r = \frac{5.95}{\sqrt{42 \times 10.64875}} = 0.2813\) | M1 A1 | |
| (b) 8 pairs \(\therefore\) + 0.2813 is only weak evidence of June getting warmer | B1 | (9 marks total) |
(a) Scatter diagram with points plotted | B3 |
(b) $S_{YY} = 140 - \frac{28^2}{8} = 42$ | M1 |
$S_{YY} = 4173.93 - \frac{182.5^2}{8} = 10.64875$ | M1 |
$S_{YY} = 644.7 - \frac{28 \times 182.5}{8} = 5.95$ | M1 |
$r = \frac{5.95}{\sqrt{42 \times 10.64875}} = 0.2813$ | M1 A1 |
(b) 8 pairs $\therefore$ + 0.2813 is only weak evidence of June getting warmer | B1 | (9 marks total)\begin{enumerate}[label=(\alph*)]
\item Plot a scatter diagram showing these data.
The student wanted to investigate further whether or not her data provided evidence of an increase in temperature in June each year. Using $Y$ for the number of years since 1993 and $T$ for the mean temperature, she calculated the following summary statistics.
$$\Sigma Y = 28 , \quad \Sigma T = 182.5 , \quad \Sigma Y ^ { 2 } = 140 , \quad \Sigma T ^ { 2 } = 4173.93 , \quad \Sigma Y T = 644.7 .$$
\item Calculate the product moment correlation coefficient for these data.
\item Comment on your result in relation to the student's enquiry.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [9]}}