| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Moderate -0.8 This is a straightforward histogram question with unequal class widths requiring frequency density calculation, plus a simple median location using cumulative frequency. Both are standard S1 techniques with no problem-solving or novel insight required—easier than average A-level. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Lifetime \(( x\) hours \()\) | \(0 < x \leqslant 20\) | \(20 < x \leqslant 30\) | \(30 < x \leqslant 50\) | \(50 < x \leqslant 65\) | \(65 < x \leqslant 100\) |
| Frequency | 24 | 13 | 14 | 21 | 18 |
| Answer | Marks | Guidance |
|---|---|---|
| Lifetime (x hours) | Frequency | Width |
| \(0 < x \leq 20\) | 24 | 20 |
| \(20 < x \leq 30\) | 13 | 10 |
| \(30 < x \leq 50\) | 14 | 20 |
| \(50 < x \leq 65\) | 21 | 15 |
| \(65 < x \leq 100\) | 18 | 35 |
| M1 for fds, A1 CAO | ||
| Accept any suitable unit for fd such as eg freq per 10 hours. | ||
| L1 linear scales on both axes and label on vert axis | ||
| W1 width of bars, H1 height of bars | 5 marks | |
| (ii) Median lies in third class interval \((30 < x \leq 50)\) | B1 CAO | |
| Median = 45.5th lifetime (which lies beyond 37 but not as far as 51) | E1 dep on B1 | 2 marks |
**(i)**
| Lifetime (x hours) | Frequency | Width | FD |
|---|---|---|---|
| $0 < x \leq 20$ | 24 | 20 | 1.2 |
| $20 < x \leq 30$ | 13 | 10 | 1.3 |
| $30 < x \leq 50$ | 14 | 20 | 0.7 |
| $50 < x \leq 65$ | 21 | 15 | 1.4 |
| $65 < x \leq 100$ | 18 | 35 | 0.51 |
| M1 for fds, A1 CAO |
Accept any suitable unit for fd such as eg freq per 10 hours. |
| L1 linear scales on both axes and label on vert axis |
| W1 width of bars, H1 height of bars | 5 marks
**(ii)** Median lies in third class interval $(30 < x \leq 50)$ | B1 CAO |
Median = 45.5th lifetime (which lies beyond 37 but not as far as 51) | E1 dep on B1 | 2 marks
**TOTAL: 7 marks**
---3 The lifetimes in hours of 90 components are summarised in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Lifetime $( x$ hours $)$ & $0 < x \leqslant 20$ & $20 < x \leqslant 30$ & $30 < x \leqslant 50$ & $50 < x \leqslant 65$ & $65 < x \leqslant 100$ \\
\hline
Frequency & 24 & 13 & 14 & 21 & 18 \\
\hline
\end{tabular}
\end{center}
(i) Draw a histogram to illustrate these data.\\
(ii) In which class interval does the median lie? Justify your answer.
\hfill \mbox{\textit{OCR MEI S1 2010 Q3 [7]}}