| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Standard +0.3 This is a standard S1 correlation and regression question requiring straightforward application of formulas for PMCC and regression line, followed by prediction and interpretation. All calculations are routine with given summations; the only mild challenge is computing Syy from the data and recognizing extrapolation concerns, making it slightly easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09e Use regression: for estimation in context |
| Contestant | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Judge 1 (\(x\)) | 43 | 32 | 40 | 21 | 47 | 11 | 29 | 38 |
| Judge 2 (\(y\)) | 39 | 25 | 40 | 22 | 36 | 13 | 27 | 32 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\sum y = 234\), \(\sum y^2 = 7448\) | B1 B1 | |
| \(S_{xx} = 1013·875\), \(S_{xy} = 603·5\), \(S_{yy} = 738·75\) | M1 A1 A1 | |
| \(r = 0·944\) | ||
| (b) \(x - \frac{261}{8} = \frac{738·75}{603·5}(y - \frac{234}{8})\) → \(x = 1·22y - 3·18\) | M1 M1 A1 A1 | |
| (c) Approx. 52 | M1 A1 | |
| (d) Quite good, as \(r\) is fairly close to 1 | B1 B1 | 13 marks total |
(a) $\sum y = 234$, $\sum y^2 = 7448$ | B1 B1 |
$S_{xx} = 1013·875$, $S_{xy} = 603·5$, $S_{yy} = 738·75$ | M1 A1 A1 |
$r = 0·944$ | |
(b) $x - \frac{261}{8} = \frac{738·75}{603·5}(y - \frac{234}{8})$ → $x = 1·22y - 3·18$ | M1 M1 A1 A1 |
(c) Approx. 52 | M1 A1 |
(d) Quite good, as $r$ is fairly close to 1 | B1 B1 | 13 marks totalThe following marks out of 50 were given by two judges to the contestants in a talent contest:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
Contestant & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ \\
\hline
Judge 1 ($x$) & 43 & 32 & 40 & 21 & 47 & 11 & 29 & 38 \\
\hline
Judge 2 ($y$) & 39 & 25 & 40 & 22 & 36 & 13 & 27 & 32 \\
\hline
\end{tabular}
Given that $\sum x = 261$, $\sum x^2 = 9529$ and $\sum xy = 8373$,
\begin{enumerate}[label=(\alph*)]
\item calculate the product-moment correlation coefficient between the two judges' marks [5 marks]
\item Find an equation of the regression line of $x$ on $y$. [4 marks]
\end{enumerate}
Contestant $I$ was awarded 45 marks by Judge 2.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Estimate the mark that this contestant would have received from Judge 1. [2 marks]
\item Comment, with explanation, on the probable accuracy of your answer. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [13]}}