| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then estimate mean/standard deviation |
| Difficulty | Moderate -0.8 This is a routine S1 statistics question requiring standard procedures: drawing a histogram with unequal class widths (requiring frequency density calculation) and computing mean/standard deviation from grouped data using midpoints. Both are textbook exercises with no problem-solving or conceptual challenge beyond careful arithmetic. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Marks | \(1 - 20\) | \(21 - 30\) | \(31 - 40\) | \(41 - 50\) | \(51 - 60\) | \(61 - 75\) |
| Frequency | 40 | 34 | 56 | 54 | 29 | 21 |
6 The following table gives the marks, out of 75, in a pure mathematics examination taken by 234 students.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Marks & $1 - 20$ & $21 - 30$ & $31 - 40$ & $41 - 50$ & $51 - 60$ & $61 - 75$ \\
\hline
Frequency & 40 & 34 & 56 & 54 & 29 & 21 \\
\hline
\end{tabular}
\end{center}
(i) Draw a histogram on graph paper to represent these results.\\
(ii) Calculate estimates of the mean mark and the standard deviation.
\hfill \mbox{\textit{CAIE S1 2009 Q6 [9]}}