| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| 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 the standard procedure of calculating frequency densities for unequal class widths and drawing bars. Part (ii) asks for basic descriptive observations (e.g., 'positively skewed', 'modal class'). No problem-solving or conceptual insight required—pure recall and application of a textbook method. |
| Spec | 2.02b Histogram: area represents frequency |
| Time ( \(t\) minutes) | \(40 \leqslant t < 45\) | \(45 \leqslant t < 50\) | \(50 \leqslant t < 60\) | \(60 \leqslant t < 70\) | \(70 \leqslant t < 90\) |
| Number of CDs | 26 | 18 | 31 | 16 | 9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Frequency densities: \(40-\): 5.2, \(45-\): 3.6, \(50-\): 3.1, \(60-\): 1.6, \(70-\): 0.45 | M1, A1 | Calculation of fd's (accept values in proportion) |
| Linear scales on axes | G1 | Linear scales |
| Correct widths of bars | G1 | Widths of bars |
| Correct heights of bars | G1 | Heights of bars |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| e.g. The distribution is positively skewed | E1 | |
| The mode is at the extreme left of the distribution. Accept range = 50 or median = 52 | E1 |
## Question 1:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Frequency densities: $40-$: 5.2, $45-$: 3.6, $50-$: 3.1, $60-$: 1.6, $70-$: 0.45 | M1, A1 | Calculation of fd's (accept values in proportion) |
| Linear scales on axes | G1 | Linear scales |
| Correct widths of bars | G1 | Widths of bars |
| Correct heights of bars | G1 | Heights of bars |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| e.g. The distribution is positively skewed | E1 | |
| The mode is at the extreme left of the distribution. Accept range = 50 or median = 52 | E1 | |
---1 The number of minutes of recorded music on a sample of 100 CDs is summarised below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time ( $t$ minutes) & $40 \leqslant t < 45$ & $45 \leqslant t < 50$ & $50 \leqslant t < 60$ & $60 \leqslant t < 70$ & $70 \leqslant t < 90$ \\
\hline
Number of CDs & 26 & 18 & 31 & 16 & 9 \\
\hline
\end{tabular}
\end{center}
(i) Illustrate the data by means of a histogram.\\
(ii) Identify two features of the distribution.
\hfill \mbox{\textit{OCR MEI S1 2005 Q1 [7]}}