| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Find missing data values |
| Difficulty | Moderate -0.3 This is a standard S1 correlation and regression question requiring routine application of formulas for PMCC, regression line, and prediction. Part (a) is trivial arithmetic, parts (b)-(c) involve substituting given summations into standard formulas, and parts (d)-(e) test basic interpretation. While computational, it requires no problem-solving insight beyond textbook procedures, making it slightly easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
| Geography (\(x\)) | 34 | 57 | 49 | 21 | 84 | 53 | 10 | 77 | 61 | 85 |
| History (\(y\)) | 40 | 49 | 55 | 40 | 71 | 39 | 47 | 65 | 73 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(547 - 479 = 68\) | B1 | |
| (b) \(\sum x = 531\) | B1 | |
| \(S_{xx} = 5890.8\), \(S_{yy} = 1654.1\), \(S_{xy} = 2296.3\) | M1 A1 A1 | |
| \(r = 0.736\) | M1 A1 | |
| (c) \(y - 54.7 = (2296.3/5890.8)(x - 53.1) = 0.3898x - 20.699\) | M1 A1 | |
| \(y = 0.390x + 34.0\) | M1 A1 | |
| (d) When \(x = 70\), \(y \simeq 61.3\) | M1 A1 | |
| (e) Not very reliable, as value of \(r\) shows only moderate correlation | B1 B1 | Total: 13 |
(a) $547 - 479 = 68$ | B1 |
(b) $\sum x = 531$ | B1 |
$S_{xx} = 5890.8$, $S_{yy} = 1654.1$, $S_{xy} = 2296.3$ | M1 A1 A1 |
$r = 0.736$ | M1 A1 |
(c) $y - 54.7 = (2296.3/5890.8)(x - 53.1) = 0.3898x - 20.699$ | M1 A1 |
$y = 0.390x + 34.0$ | M1 A1 |
(d) When $x = 70$, $y \simeq 61.3$ | M1 A1 |
(e) Not very reliable, as value of $r$ shows only moderate correlation | B1 B1 | **Total: 13**The marks obtained by ten students in a Geography test and a History test were as follows:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Student & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Geography ($x$) & 34 & 57 & 49 & 21 & 84 & 53 & 10 & 77 & 61 & 85 \\
\hline
History ($y$) & 40 & 49 & 55 & 40 & & 71 & 39 & 47 & 65 & 73 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Given that $\sum y = 547$, calculate the mark obtained by student $E$ in History. [1 mark]
Given further that $\sum x^2 = 34087$, $\sum y^2 = 31575$ and $\sum xy = 31342$, calculate
\item the product moment correlation coefficient between $x$ and $y$, [4 marks]
\item an equation of the regression line of $y$ on $x$, [4 marks]
\item an estimate of the History mark of student $K$, who scored 70 in Geography. [2 marks]
\item State, with a reason, whether you would expect your answer to part (d) to be reliable. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [13]}}