| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2019 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw back-to-back stem-and-leaf diagram |
| Difficulty | Easy -1.8 This is a straightforward data representation question requiring only mechanical sorting and plotting of given data into a standard diagram format, followed by basic statistical calculations (median and IQR) from ordered data. No problem-solving, conceptual understanding, or multi-step reasoning is needed—purely routine procedural work well below average A-level difficulty. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Dolphins | 62 | 75 | 69 | 82 | 63 | 80 | 65 | 65 | 73 | 82 | 72 |
| Sharks | 68 | 84 | 59 | 70 | 71 | 64 | 77 | 80 | 66 | 74 | 72 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct stem (5, 6, 7, 8) | B1 | Correct stem can be upside down, ignore extra values |
| Correct Dolphin leaves on LHS | B1 | Correct Dolphin must be on LHS |
| Correct Sharks leaves; Key: \(3\ | 6\ | 4\) means 63 kg for Dolphins and 64 kg for Sharks |
| Single key for their single diagram, both teams identified and 'kg' stated | B1FT | Need both teams identified and 'kg' stated at least once |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 72\), \(LQ = 65\), \(UQ = 80\) | B1 | \(72 < UQ < 82 - 62 < LQ < 72\) |
| \(IQR = 80 - 65\) | M1 | nfww |
| \(= 15\) | A1 | SCB1 if M0 scored for \(LQ = 65\) and \(UQ = 80\) |
## Question 5:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct stem (5, 6, 7, 8) | B1 | Correct stem can be upside down, ignore extra values |
| Correct Dolphin leaves on LHS | B1 | Correct Dolphin must be on LHS |
| Correct Sharks leaves; Key: $3\|6\|4$ means 63 kg for Dolphins and 64 kg for Sharks | B1 | Correct Sharks on either LHS or RHS. Alignment $\pm$ half a space, no late entries squeezed in |
| Single key for their single diagram, both teams identified and 'kg' stated | B1FT | Need both teams identified and 'kg' stated at least once |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 72$, $LQ = 65$, $UQ = 80$ | B1 | $72 < UQ < 82 - 62 < LQ < 72$ |
| $IQR = 80 - 65$ | M1 | nfww |
| $= 15$ | A1 | SCB1 if M0 scored for $LQ = 65$ and $UQ = 80$ |
---5 The weights, in kg, of the 11 members of the Dolphins swimming team and the 11 members of the Sharks swimming team are shown below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Dolphins & 62 & 75 & 69 & 82 & 63 & 80 & 65 & 65 & 73 & 82 & 72 \\
\hline
Sharks & 68 & 84 & 59 & 70 & 71 & 64 & 77 & 80 & 66 & 74 & 72 \\
\hline
\end{tabular}
\end{center}
(i) Draw a back-to-back stem-and-leaf diagram to represent this information, with Dolphins on the left-hand side of the diagram and Sharks on the right-hand side.\\
(ii) Find the median and interquartile range for the Dolphins.\\
\hfill \mbox{\textit{CAIE S1 2019 Q5 [7]}}