| 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 parts are routine textbook exercises with no problem-solving or novel insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b 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 |
|---|---|---|
| Answer | Marks | Guidance |
| Frequency densities: \(\frac{34}{5}=6.8\), \(\frac{153}{5}=30.6\), \(\frac{188}{10}=18.8\), \(\frac{73}{10}=7.3\), \(\frac{27}{10}=2.7\), \(\frac{5}{20}=0.25\) | M1 | For fds |
| A1 CAO | Accept any suitable unit for fd such as freq per 5 mins | |
| Linear scales on both axes and label | G1 | |
| Correct width of bars | G1 | |
| Correct height of bars | G1 | |
| [5] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Positive skewness | B1 CAO | indep |
| [1] |
## Question 6:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequency densities: $\frac{34}{5}=6.8$, $\frac{153}{5}=30.6$, $\frac{188}{10}=18.8$, $\frac{73}{10}=7.3$, $\frac{27}{10}=2.7$, $\frac{5}{20}=0.25$ | M1 | For fds |
| | A1 CAO | Accept any suitable unit for fd such as freq per 5 mins |
| Linear scales on both axes and label | G1 | |
| Correct width of bars | G1 | |
| Correct height of bars | G1 | |
| | **[5]** | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Positive skewness | B1 CAO | indep |
| | **[1]** | |6 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 Q6 [6]}}