| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate frequency density from frequency |
| Difficulty | Moderate -0.8 This is a straightforward S1 question testing basic understanding of statistical diagrams. Part (i) requires simple frequency density calculation (frequency รท class width), part (ii) needs cumulative frequency coordinates (standard procedure), and part (iii) tests conceptual understanding that grouped data prevents exact quartile calculation. All parts are routine recall and application of standard techniques with no problem-solving or novel insight required. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02h Recognize outliers |
| \(x\) | \(10 \leqslant x \leqslant 19\) | \(20 \leqslant x \leqslant 24\) | \(25 \leqslant x \leqslant 29\) | \(30 \leqslant x \leqslant 49\) |
| Number of stones | 25 | 22 | 29 | 24 |
### Part i
**Answer:** $\frac{2y}{10} = 2.5$
**Marks:** M1, A1 2
**Guidance:** Allow $\frac{2y}{(96t0)}$ or 2.78: M1
### Part ii
**Answer:** (19.5, 25) and (9.5, 0)
**Marks:** B1, B1 2
**Guidance:** Allow (24.5, 47). Both reversed: SC B1. If three given, ignore (24.5, 47)
### Part iii
**Answer:** Don't know exact or specific values of $x$ (or min or max or quartiles or median or whiskers). oe Can only estimate (min or max or quartiles or median or whiskers) oe Can't work out (.....) oe Data is grouped oe
**Marks:** B1 1
**Guidance:** Exact data not known. Allow because data is rounded
---The diameters of 100 pebbles were measured. The measurements rounded to the nearest millimetre, $x$, are summarised in the table.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & $10 \leqslant x \leqslant 19$ & $20 \leqslant x \leqslant 24$ & $25 \leqslant x \leqslant 29$ & $30 \leqslant x \leqslant 49$ \\
\hline
Number of stones & 25 & 22 & 29 & 24 \\
\hline
\end{tabular}
\end{center}
These data are to be presented on a statistical diagram.
\begin{enumerate}[label=(\roman*)]
\item For a histogram, find the frequency density of the $10 \leqslant x \leqslant 19$ class. [2]
\item For a cumulative frequency graph, state the coordinates of the first two points that should be plotted. [2]
\item Why is it not possible to draw an exact box-and-whisker plot to illustrate the data? [1]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q5 [5]}}