| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram from frequency table |
| Difficulty | Easy -1.8 This is a routine, mechanical task requiring only recall of histogram construction with unequal class widths (calculating frequency density) and basic identification of skewness from a visual distribution. No problem-solving, interpretation challenges, or multi-step reasoning required—purely procedural application of standard techniques. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| 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: \(6.8, 30.6, 18.8, 7.3, 2.7, 0.25\) | M1, A1 CAO | M1 for fds; accept any suitable unit for fd such as freq per 5 mins |
| Histogram with correct linear scales, labels and bar widths | G1, G1 | G1 linear scales on both axes and label; G1 width of bars |
| Correct bar heights | G1 | G1 height of bars |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Positive skewness | B1 CAO (indep) |
# Question 3:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequency densities: $6.8, 30.6, 18.8, 7.3, 2.7, 0.25$ | M1, A1 CAO | M1 for fds; accept any suitable unit for fd such as freq per 5 mins |
| Histogram with correct linear scales, labels and bar widths | G1, G1 | G1 linear scales on both axes and label; G1 width of bars |
| Correct bar heights | G1 | G1 height of bars |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Positive skewness | B1 CAO (indep) | |
---3 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 2007 Q3 [6]}}