| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| 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 application of the correlation coefficient formula using given summary statistics (Sxx, Syy, Sxy). Part (a) is direct substitution into r = Sxy/√(Sxx·Syy), part (b) tests understanding that linear coding doesn't affect correlation (a standard S1 result), and part (c) requires basic interpretation. All parts are routine recall and standard procedures with no problem-solving or novel insight required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08b Linear coding: effect on pmcc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(S_{xy} = 23070 - \frac{477 \times 480}{12} = 3990\) | B1 | Correct expression for \(S_{xy}\) |
| \(r = \frac{\text{"3990"}}{\sqrt{5606.25 \times 4244}}\) | M1 | Correct attempt at \(r\) f.t. their 3990; but \(\frac{23070}{\sqrt{5606.25 \times 4244}}\) is M0 |
| \(= 0.81799...\) awrt \(0.818\) | A1 | If answer 0.82 only seen then B1M1A0 can be given |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(0.818\) | B1ft | For awrt 0.818 or f.t. answer to (a) for \( |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Positive correlation, or value of \(r\) is close to 1, or value of \(r > 0\) (NOT "high/strong correlation") | B1 | 1st B1 for reason of positive correlation (allow even if \(r > 1\)); "positive skew" or "positive gradient" is B0 |
| So there is support for the bank's claim, or "increase in unemployment is accompanied by increase in house repossessions" | B1 | 2nd B1 for comment that supports the claim; marks independent but 1st B1 requires some idea of positive correlation |
| (c) SC: If \( | r | < 0.2\): 1st B1 for saying there is no or little correlation; 2nd B1 for comment that says this does not support the bank's claim |
# Question 2:
## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $S_{xy} = 23070 - \frac{477 \times 480}{12} = 3990$ | B1 | Correct expression for $S_{xy}$ |
| $r = \frac{\text{"3990"}}{\sqrt{5606.25 \times 4244}}$ | M1 | Correct attempt at $r$ f.t. their 3990; but $\frac{23070}{\sqrt{5606.25 \times 4244}}$ is M0 |
| $= 0.81799...$ awrt $0.818$ | A1 | If answer 0.82 only seen then B1M1A0 can be given |
## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.818$ | B1ft | For awrt 0.818 or f.t. answer to (a) for $|r| < 1$; allow 2sf or 1sf follow through; must be a number |
## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Positive correlation, or value of $r$ is close to 1, or value of $r > 0$ (NOT "high/strong correlation") | B1 | 1st B1 for reason of positive correlation (allow even if $r > 1$); "positive skew" or "positive gradient" is B0 |
| So there is support for the bank's claim, or "increase in unemployment is accompanied by increase in house repossessions" | B1 | 2nd B1 for comment that supports the claim; marks independent but 1st B1 requires some idea of positive correlation |
**(c) SC:** If $|r| < 0.2$: 1st B1 for saying there is no or little correlation; 2nd B1 for comment that says this does not support the bank's claim
---2. A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month. The bank codes the data using variables $x = \frac { u - 100 } { 3 }$ and $y = \frac { h - 20 } { 7 }$ The results for the 12 months of 2009 are summarised below.
$$\sum x = 477 \quad S _ { x x } = 5606.25 \quad \sum y = 480 \quad S _ { y y } = 4244 \quad \sum x y = 23070$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the product moment correlation coefficient for $x$ and $y$.
\item Write down the product moment correlation coefficient for $u$ and $h$.
The bank claims that an increase in unemployment among its customers is associated with an increase in house repossessions.
\item State, with a reason, whether or not the bank's claim is supported by these data.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2012 Q2 [6]}}