| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (unequal class widths) |
| Difficulty | Easy -1.8 This is a routine, mechanical S1 task requiring only standard procedures: calculate cumulative frequencies (simple addition), plot points, draw a smooth curve, and read off median/quartiles. No problem-solving, interpretation challenges, or conceptual depth—pure procedural recall of a basic statistical technique taught early in the specification. |
| Spec | 2.02a Interpret single variable data: tables and diagrams |
| \(0 < x \leqslant 1\) | \(1 < x \leqslant 2\) | \(2 < x \leqslant 3\) | \(3 < x \leqslant 4\) | \(4 < x \leqslant 6\) | \(6 < x \leqslant 10\) | ||
| 38 | 30 | 21 | 14 | 9 | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cumulative frequencies calculated: 38, 68, 89, 103, 112, 120 | G1 | For calculating values |
| Plotting end points correctly | G1 | Plotting end points |
| Heights including \((0,0)\) | G1 | Heights inc \((0,0)\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 1.7\) miles | B1 | |
| Lower quartile \(= 0.8\) miles | M1 | |
| Upper quartile \(= 3\) miles | M1 | |
| Interquartile range \(= 2.2\) miles | A1 ft |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The graph exhibits positive skewness | E1 |
## Question 4:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cumulative frequencies calculated: 38, 68, 89, 103, 112, 120 | G1 | For calculating values |
| Plotting end points correctly | G1 | Plotting end points |
| Heights including $(0,0)$ | G1 | Heights inc $(0,0)$ |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 1.7$ miles | B1 | |
| Lower quartile $= 0.8$ miles | M1 | |
| Upper quartile $= 3$ miles | M1 | |
| Interquartile range $= 2.2$ miles | A1 ft | |
### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| The graph exhibits positive skewness | E1 | |
---4 Answer part (i) of this question on the insert provided.
A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
\begin{tabular}{ l }
Length \\
$( x$ miles $)$ \\
\end{tabular} & $0 < x \leqslant 1$ & $1 < x \leqslant 2$ & $2 < x \leqslant 3$ & $3 < x \leqslant 4$ & $4 < x \leqslant 6$ & $6 < x \leqslant 10$ \\
\hline
\begin{tabular}{ l }
Number of \\
journeys \\
\end{tabular} & 38 & 30 & 21 & 14 & 9 & 8 \\
\hline
\end{tabular}
\end{center}
(i) On the insert, draw a cumulative frequency diagram to illustrate the data.\\
(ii) Use your graph to estimate the median length of journey and the quartiles.
Hence find the interquartile range.\\
(iii) State the type of skewness of the distribution of the data.
\hfill \mbox{\textit{OCR MEI S1 Q4 [9]}}