| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (unequal class widths) |
| Difficulty | Easy -1.3 This is a routine S1 statistics question requiring standard procedures: calculating cumulative frequencies from a frequency table, plotting points, and reading off median/quartiles. It involves no problem-solving or conceptual challenge—just mechanical application of well-practiced techniques with straightforward data. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| \(0 < x \leqslant 1\) | \(1 < x \leqslant 2\) | \(2 < x \leqslant 3\) | \(3 < x \leqslant 4\) | \(4 < x \leqslant 6\) | \(6 < x \leqslant 10\) | ||
| 38 | 30 | 21 | 14 | 9 | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Cumulative frequencies: 38, 68, 89, 103, 112, 120 | G1 | For calculating 38,68,89,103,112,120 |
| Plotting end points | G1 | Plotting end points |
| Heights including \((0,0)\) | G1 | Heights inc \((0,0)\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | 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 | Mark | Guidance |
| The graph exhibits positive skewness | E1 |
## Question 2:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Cumulative frequencies: 38, 68, 89, 103, 112, 120 | G1 | For calculating 38,68,89,103,112,120 |
| Plotting end points | G1 | Plotting end points |
| Heights including $(0,0)$ | G1 | Heights inc $(0,0)$ |
### Part (ii)
| Answer | Mark | 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 | Mark | Guidance |
|--------|------|----------|
| The graph exhibits positive skewness | E1 | |
---2 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 2005 Q2 [8]}}