| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Sketch theoretical scatter diagram |
| Difficulty | Moderate -0.8 This question tests basic understanding of correlation concepts through drawing and interpretation rather than calculation. Part (a) requires sketching scatter diagrams showing perfect positive correlation (trivial - points on a line) and weak negative correlation (straightforward visualization). Part (b) asks for conceptual understanding that sample size affects significance, which is standard S1 knowledge requiring only recall of statistical principles rather than problem-solving or computation. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | B2 | Scatter diagram showing positive correlation with points roughly linear |
| (ii) | B2 | Scatter diagram showing weak/no correlation with points scattered |
| (b) | B2, (6) | With small \(n\) weak evidence of +ve correlation; with larger \(n\) stronger evidence of +ve correlation |
(i) | B2 | Scatter diagram showing positive correlation with points roughly linear
(ii) | B2 | Scatter diagram showing weak/no correlation with points scattered
(b) | B2, (6) | With small $n$ weak evidence of +ve correlation; with larger $n$ stronger evidence of +ve correlation
---\begin{enumerate}[label=(\alph*)]
\item Draw two separate scatter diagrams, each with eight points, to illustrate the relationship between $x$ and $y$ in the cases where they have a product moment correlation coefficient equal to
\begin{enumerate}[label=(\roman*)]
\item exactly $+1$,
\item about $-0.4$. [4 marks]
\end{enumerate}
\item Explain briefly how the conclusion you would draw from a product moment correlation coefficient of $+0.3$ would vary according to the number of pairs of data used in its calculation. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q1 [6]}}