| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then perform other calculations |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring standard histogram construction with unequal class widths (calculating frequency densities) and identifying which class contains the upper quartile using cumulative frequency. Both are routine textbook exercises with no problem-solving or novel insight required, making it easier than average. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread |
| Length \(( \mathrm { cm } )\) | \(2.0 - 3.5\) | \(3.5 - 4.5\) | \(4.5 - 5.5\) | \(5.5 - 7.0\) | \(7.0 - 9.0\) |
| Frequency | 8 | 25 | 28 | 31 | 12 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| UQ \(5.5 - 7.0\) cm | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| fd values: \(5.33, 25, 28, 20.7, 6\) | M1 | Attempt at fd or scaled freq [fr/cw] |
| Correct heights on graph | A1 | Correct heights seen on graph |
| Correct bar widths, no gaps | B1 | Correct bar widths no gaps |
| Labels (fd and length/cm) and correct bar ends | B1 [4] | Labels and correct bar ends |
## Question 2:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| UQ $5.5 - 7.0$ cm | B1 [1] | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| fd values: $5.33, 25, 28, 20.7, 6$ | M1 | Attempt at fd or scaled freq [fr/cw] |
| Correct heights on graph | A1 | Correct heights seen on graph |
| Correct bar widths, no gaps | B1 | Correct bar widths no gaps |
| Labels (fd and length/cm) and correct bar ends | B1 [4] | Labels and correct bar ends |
---2 The table summarises the lengths in centimetres of 104 dragonflies.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Length $( \mathrm { cm } )$ & $2.0 - 3.5$ & $3.5 - 4.5$ & $4.5 - 5.5$ & $5.5 - 7.0$ & $7.0 - 9.0$ \\
\hline
Frequency & 8 & 25 & 28 & 31 & 12 \\
\hline
\end{tabular}
\end{center}
(i) State which class contains the upper quartile.\\
(ii) Draw a histogram, on graph paper, to represent the data.
\hfill \mbox{\textit{CAIE S1 2015 Q2 [5]}}