| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| 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 statistics question requiring basic histogram construction with unequal class widths (calculating frequency densities) and finding the median position (45th value). Both are standard S1 techniques with no problem-solving or novel insight required, making it easier than average. |
| Spec | 2.02b Histogram: area represents frequency |
| 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 |
# Question 2
## (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 frequency densities
A1 CAO
Accept any suitable unit for frequency density such as frequency per 10 hours.
L1 linear scales on both axes and label on vertical axis
W1 width of bars
H1 height of bars
**Total: 5 marks**
## (ii)
B1 Median lies in third class interval ($30 < x \leq 50$) CAO
E1 Median = 45.5th lifetime (which lies beyond 37 but not as far as 51), dependent on B1
**Total: 2 marks**
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**TOTAL FOR QUESTION 2: 7 marks**2 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 Q2 [7]}}