| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| 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 straightforward grouped data question requiring standard S1 techniques: calculating frequency densities for a histogram and using midpoints to estimate the mean. Both are routine textbook exercises with no conceptual challenges or problem-solving required, making it easier than average. |
| Spec | 2.02b Histogram: area represents frequency2.02g Calculate mean and standard deviation |
| Time spent \(( t\) hours \()\) | \(0.1 \leqslant t \leqslant 0.5\) | \(0.6 \leqslant t \leqslant 1.0\) | \(1.1 \leqslant t \leqslant 2.0\) | \(2.1 \leqslant t \leqslant 3.0\) | \(3.1 \leqslant t \leqslant 4.5\) |
| Frequency | 11 | 15 | 18 | 30 | 21 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| fd: 22, 30, 18, 30, 14 | M1 | Attempt at freq density or scaling |
| A1 | Correct heights seen on graph | |
| B1 | Bar lines correctly located at 0.55, 1.05, 2.05, 3.05, no gaps | |
| B1 | Correct widths of bars | |
| B1 5 | Both axes uniform from at least 0 to 15 or 30, and 0.05 to 4.5 and labelled (fd, or freq per half hour, time, hours, \(t\)) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| mid-points 0.3, 0.8, 1.55, 2.55, 3.8 | M1 | An attempt at mid-points (not class widths) |
| \(= 199.5 / 95\) | M1 | Using \((\Sigma \text{ their } fx) /\) their 95 |
| mean \(= 2.1\) hours | A1 3 | Correct answer from 199.5 in num |
## Question 5:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| fd: 22, 30, 18, 30, 14 | M1 | Attempt at freq density or scaling |
| | A1 | Correct heights seen **on graph** |
| | B1 | Bar lines correctly located at 0.55, 1.05, 2.05, 3.05, no gaps |
| | B1 | Correct widths of bars |
| | B1 **5** | Both axes uniform from at least 0 to 15 or 30, and 0.05 to 4.5 and labelled (fd, or freq per half hour, time, hours, $t$) |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| mid-points 0.3, 0.8, 1.55, 2.55, 3.8 | M1 | An attempt at mid-points (not class widths) |
| $= 199.5 / 95$ | M1 | Using $(\Sigma \text{ their } fx) /$ their 95 |
| mean $= 2.1$ hours | A1 **3** | Correct answer from 199.5 in num |
---5 As part of a data collection exercise, members of a certain school year group were asked how long they spent on their Mathematics homework during one particular week. The times are given to the nearest 0.1 hour. The results are displayed in the following table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time spent $( t$ hours $)$ & $0.1 \leqslant t \leqslant 0.5$ & $0.6 \leqslant t \leqslant 1.0$ & $1.1 \leqslant t \leqslant 2.0$ & $2.1 \leqslant t \leqslant 3.0$ & $3.1 \leqslant t \leqslant 4.5$ \\
\hline
Frequency & 11 & 15 & 18 & 30 & 21 \\
\hline
\end{tabular}
\end{center}
(i) Draw, on graph paper, a histogram to illustrate this information.\\
(ii) Calculate an estimate of the mean time spent on their Mathematics homework by members of this year group.
\hfill \mbox{\textit{CAIE S1 2008 Q5 [8]}}