| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2003 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.8 This is a routine S1 correlation calculation with coding provided. All summations are given, requiring only substitution into standard formulas for Sxx, Syy, Sxy and r. Part (c) tests understanding that linear coding doesn't affect correlation. Straightforward bookwork with no problem-solving or insight required. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r |
| \(p\) | \(q\) | |
| Monday | 4760 | 5380 |
| Tuesday | 5395 | 4460 |
| Wednesday | 5840 | 4640 |
| Thursday | 4650 | 5450 |
| Friday | 5365 | 4340 |
| Saturday | 4990 | 5550 |
| Sunday | 4365 | 5840 |
| Answer | Marks | Guidance |
|---|---|---|
| \(S_{xx} = 204.95 - \frac{48.1 \times 52.8}{7} = -157.86142\) | M1 A1 | (awrt −157.9) |
| \(S_{xx} = 155.92428\) | A1 | (awrt 155.9) |
| \(S_{yy} = 214.95714\) | A1 | (awrt 215.0) |
| (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = \frac{-157.86142}{\sqrt{155.92428... \times 214.95714}}\) | M1 A1 ft | |
| \(= -0.862269\) | A1 | (awrt −0.862) |
| (3 marks) |
| Answer | Marks |
|---|---|
| \(-0.862\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| As sales at on petrol station increases, the other decreases; limited pool of customers; close one garage | B1 | (2 marks) |
| (9 marks) |
**(a)**
| $S_{xx} = 204.95 - \frac{48.1 \times 52.8}{7} = -157.86142$ | M1 A1 | (awrt −157.9) |
| $S_{xx} = 155.92428$ | A1 | (awrt 155.9) |
| $S_{yy} = 214.95714$ | A1 | (awrt 215.0) |
| | | (4 marks) |
**(b)**
| $r = \frac{-157.86142}{\sqrt{155.92428... \times 214.95714}}$ | M1 A1 ft | |
| $= -0.862269$ | A1 | (awrt −0.862) |
| | | (3 marks) |
**(c)(i)**
| $-0.862$ | B1 | |
**(ii)**
| As sales at on petrol station increases, the other decreases; limited pool of customers; close one garage | B1 | (2 marks) |
| | | (9 marks) |
---3. A company owns two petrol stations $P$ and $Q$ along a main road. Total daily sales in the same week for $P ( \pounds p )$ and for $Q ( \pounds q )$ are summarised in the table below.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
& $p$ & $q$ \\
\hline
Monday & 4760 & 5380 \\
\hline
Tuesday & 5395 & 4460 \\
\hline
Wednesday & 5840 & 4640 \\
\hline
Thursday & 4650 & 5450 \\
\hline
Friday & 5365 & 4340 \\
\hline
Saturday & 4990 & 5550 \\
\hline
Sunday & 4365 & 5840 \\
\hline
\end{tabular}
\end{center}
When these data are coded using $x = \frac { p - 4365 } { 100 }$ and $y = \frac { q - 4340 } { 100 }$,
$$\Sigma x = 48.1 , \Sigma y = 52.8 , \Sigma x ^ { 2 } = 486.44 , \Sigma y ^ { 2 } = 613.22 \text { and } \Sigma x y = 204.95 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate $S _ { x y } , S _ { x x }$ and $S _ { y y }$.
\item Calculate, to 3 significant figures, the value of the product moment correlation coefficient between $x$ and $y$.
\item \begin{enumerate}[label=(\roman*)]
\item Write down the value of the product moment correlation coefficient between $p$ and $q$.
\item Give an interpretation of this value.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2003 Q3 [10]}}