| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | November |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Misleading visual representation features |
| Difficulty | Moderate -0.8 This is a straightforward recall question testing basic histogram principles. Students only need to identify that (1) frequency density should be used instead of frequency on the y-axis, and (2) bars should have no gaps. These are standard textbook facts about histograms with unequal class widths, requiring no calculation or problem-solving. |
| Spec | 2.02b Histogram: area represents frequency |
| Distance from college \(( \mathrm { km } )\) | \(1 - 3\) | \(4 - 5\) | \(6 - 8\) | \(9 - 11\) | \(12 - 16\) |
| Number of students | 18 | 13 | 8 | 12 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| bars are not touching oe | B1 | Sensible reason involving not touching, no gaps, class boundaries, group data not continuous (may be the negative) |
| Area not rep by frequency, not used fd, not labelled fd | B1 | Must be frequency density oe. Wrong height not sufficient. (Best 2 reasons awarded) |
bars are not touching oe | B1 | Sensible reason involving not touching, no gaps, class boundaries, group data not continuous (may be the negative)
Area not rep by frequency, not used fd, not labelled fd | B1 | Must be frequency density oe. Wrong height not sufficient. (Best 2 reasons awarded)1 The distance of a student's home from college, correct to the nearest kilometre, was recorded for each of 55 students. The distances are summarised in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Distance from college $( \mathrm { km } )$ & $1 - 3$ & $4 - 5$ & $6 - 8$ & $9 - 11$ & $12 - 16$ \\
\hline
Number of students & 18 & 13 & 8 & 12 & 4 \\
\hline
\end{tabular}
\end{center}
Dominic is asked to draw a histogram to illustrate the data. Dominic's diagram is shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{d6836b62-75e7-410e-ab1e-83c391b85948-2_1225_1303_628_422}
Give two reasons why this is not a correct histogram.
\hfill \mbox{\textit{CAIE S1 2013 Q1 [2]}}