| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring a standard histogram with unequal class widths (requiring frequency density calculation) and identification of skewness from the shape. Both are routine textbook exercises with no problem-solving or novel insight required. |
| Spec | 2.02b Histogram: area represents frequency |
| Time \(( t\) minutes \()\) | \(0 \leqslant t < 5\) | \(5 \leqslant t < 10\) | \(10 \leqslant t < 20\) | \(20 \leqslant t < 30\) | \(30 \leqslant t < 40\) | \(40 \leqslant t < 60\) |
| Frequency | 34 | 153 | 188 | 73 | 27 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| time | freq | width |
| \(0-\) | 5 | 5 |
| \(5-\) | 10 | 5 |
| \(10-\) | 20 | 10 |
| \(20-\) | 30 | 10 |
| \(30-\) | 40 | 10 |
| \(40\) | 50 | 20 |
| M1 | for fds | |
| A1 | CAO |
| Answer | Marks |
|---|---|
| G1 | linear scales on both axes and label |
| G1 | width of bars |
| G1 | height of bars |
| Answer | Marks |
|---|---|
| B1 | CAO (indep) |
# Question 5:
## Part (i)
| time | freq | width | f dens |
|------|------|-------|--------|
| $0-$ | 5 | 5 | 6.8 |
| $5-$ | 10 | 5 | 30.6 |
| $10-$ | 20 | 10 | 18.8 |
| $20-$ | 30 | 10 | 7.3 |
| $30-$ | 40 | 10 | 2.7 |
| $40$ | 50 | 20 | 0.25 |
| M1 | for fds |
| A1 | CAO |
Accept any suitable unit for fd such as eg freq per 5 mins.
| G1 | linear scales on both axes and label |
| G1 | width of bars |
| G1 | height of bars |
**Total: 5 marks**
## Part (ii)
Positive skewness
| B1 | CAO (indep) |
**Total: 1 mark**5 The times taken for 480 university students to travel from their accommodation to lectures are summarised below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Time $( t$ minutes $)$ & $0 \leqslant t < 5$ & $5 \leqslant t < 10$ & $10 \leqslant t < 20$ & $20 \leqslant t < 30$ & $30 \leqslant t < 40$ & $40 \leqslant t < 60$ \\
\hline
Frequency & 34 & 153 & 188 & 73 & 27 & 5 \\
\hline
\end{tabular}
\end{center}
(i) Illustrate these data by means of a histogram.\\
(ii) Identify the type of skewness of the distribution.
\hfill \mbox{\textit{OCR MEI S1 Q5 [6]}}