| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2022 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward S1 correlation question requiring direct application of the formula r = S_dp/√(S_dd × S_pp) with given summary statistics. Parts (b) and (c) test basic understanding that linear transformations preserve |r| and correlation is unaffected by such relationships. All calculations are routine with no problem-solving or conceptual challenges beyond standard textbook exercises. |
| Spec | 2.02g Calculate mean and standard deviation5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Scheme | Marks |
| (a) | \(S_{\phi} = 5240.8 - \frac{1029 \times 50.8}{10} [= 13.48]\) | M1 |
| \(r = \frac{-13.48'}{\sqrt{344.9 \times 0.576}} = 0.9563834526\ldots\) | M1 | 2nd M1 valid attempt at \(r\) with their \(S_{\phi}\) not equal to 5240.8 and the correct denominator |
| awrt 0.956 | A1 (3) | A1 awrt 0.956 |
| (b)(i) | \(w = 50 - p\) | B1 (2) |
| (ii) | \(-1\) | B1 |
| (c) | \(-0.956\) | B1ft (1) |
| Part | Scheme | Marks | Guidance |
|------|--------|-------|----------|
| (a) | $S_{\phi} = 5240.8 - \frac{1029 \times 50.8}{10} [= 13.48]$ | M1 | 1st M1 correct expression for $S_{\phi}$ |
| | $r = \frac{-13.48'}{\sqrt{344.9 \times 0.576}} = 0.9563834526\ldots$ | M1 | 2nd M1 valid attempt at $r$ with their $S_{\phi}$ not equal to 5240.8 and the correct denominator |
| | awrt **0.956** | A1 (3) | A1 awrt 0.956 |
| (b)(i) | $w = 50 - p$ | B1 (2) | B1 allow equivalent rearrangements |
| (ii) | $-1$ | B1 | B1 – 1 cao |
| (c) | $-0.956$ | B1ft (1) | B1ft follow through $-1 \times$ their(a) providing $-1 < $ their (a) $< 1$ |
---2. Tom's car holds 50 litres of petrol when the fuel tank is full.
For each of 10 journeys, each starting with 50 litres of petrol in the fuel tank, Tom records the distance travelled, $d$ kilometres, and the amount of petrol used, $p$ litres.
The summary statistics for the 10 journeys are given below.
$$\sum d = 1029 \quad \sum p = 50.8 \quad \sum d p = 5240.8 \quad \mathrm {~S} _ { d d } = 344.9 \quad \mathrm {~S} _ { p p } = 0.576$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the product moment correlation coefficient between $d$ and $p$
The amount of petrol remaining in the fuel tank for each journey, $w$ litres, is recorded.
\item \begin{enumerate}[label=(\roman*)]
\item Write down an equation for $w$ in terms of $p$
\item Hence, write down the value of the product moment correlation coefficient between $w$ and $p$
\end{enumerate}\item Write down the value of the product moment correlation coefficient between $d$ and $w$
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\hfill \mbox{\textit{Edexcel S1 2022 Q2 [6]}}