| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Complete frequency table from histogram only |
| Difficulty | Moderate -0.8 This is a routine histogram interpretation question requiring students to apply the formula frequency = frequency density × class width, then calculate a mean from grouped data and a basic probability. These are standard S1 techniques with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature and potential for arithmetic errors. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02g Calculate mean and standard deviation2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Time \(( t\) minutes \()\) | \(2 < t \leqslant 4\) | \(4 < t \leqslant 6\) | \(6 < t \leqslant 7\) | \(7 < t \leqslant 8\) | \(8 < t \leqslant 10\) | \(10 < t \leqslant 16\) |
| Frequency |
5 The following histogram illustrates the distribution of times, in minutes, that some students spent taking a shower.\\
\includegraphics[max width=\textwidth, alt={}, center]{ec425eaf-8afc-4671-9ef3-ba2477b884ef-3_1031_1326_372_406}\\
(i) Copy and complete the following frequency table for the data.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | }
\hline
Time $( t$ minutes $)$ & $2 < t \leqslant 4$ & $4 < t \leqslant 6$ & $6 < t \leqslant 7$ & $7 < t \leqslant 8$ & $8 < t \leqslant 10$ & $10 < t \leqslant 16$ \\
\hline
Frequency & & & & & & \\
\hline
\end{tabular}
\end{center}
(ii) Calculate an estimate of the mean time to take a shower.\\
(iii) Two of these students are chosen at random. Find the probability that exactly one takes between 7 and 10 minutes to take a shower.
\hfill \mbox{\textit{CAIE S1 2010 Q5 [8]}}