| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct back-to-back stem-and-leaf from raw data |
| Difficulty | Easy -1.3 This is a routine data handling question requiring standard procedures: constructing a back-to-back stem-and-leaf diagram (straightforward ordering and organization), finding IQR using quartile positions (direct calculation), and using the mean formula to find a missing value (simple algebra). All three parts are textbook exercises with no problem-solving or conceptual challenge beyond basic statistical definitions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Team \(A\) | 97 | 98 | 104 | 84 | 100 | 109 | 115 | 99 | 122 | 82 | 116 | 96 | 84 | 107 | 91 |
| Team \(B\) | 75 | 79 | 94 | 101 | 96 | 77 | 111 | 108 | 83 | 84 | 86 | 115 | 82 | 113 | 95 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Back-to-back stem-and-leaf diagram with stems 7–12, team A on LHS | B1 | Correct stem, can be upside down, ignore extra values, allow 70, 80 etc with suitable numerical key |
| Team A: `4 4 2 | 8`, `9 8 7 6 1 | 9`, `9 7 4 0 |
| Team B: `7 | 5 7 9`, `8 | 2 3 4 6`, `9 |
| key \(1 \mid 9 \mid 4\) means 91 kg for team A and 94 kg for B | B1 (4) | Correct key or keys for their diagram/s, need both teams, at least one kg |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(LQ = 91\), \(UQ = 109\), \(IQ\ \text{range} = 18\) | B1 | Both quartiles correct |
| B1\(\checkmark\) (2) | Correct IQR ft wrong quartiles, \(LQ < UQ\), not \(12-4\) etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\Sigma x_{15} = 1399\) | M1 | Attempt at \(\Sigma x_{15}\) for either team |
| \(\Sigma x_{16} = 16 \times 93.9 = 1502.4\) | M1 | Mult 93.9 by 16 attempt |
| New wt \(= 1502.4 - 1399 = 103\ (103.4)\) | A1 (3) | Correct answer |
## Question 5:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Back-to-back stem-and-leaf diagram with stems 7–12, team A on LHS | B1 | Correct stem, can be upside down, ignore extra values, allow 70, 80 etc with suitable numerical key |
| Team A: `4 4 2 | 8`, `9 8 7 6 1 | 9`, `9 7 4 0 | 10`, `6 5 | 11`, `2 | 12` | B1 | Correct team A on LHS, alignment $\pm$ half a space, no late entries squeezed in, no crossing out if shape changed |
| Team B: `7 | 5 7 9`, `8 | 2 3 4 6`, `9 | 4 5 6`, `10 | 1 8`, `11 | 1 3 5`, `12 |` | B1 | Correct team B in single diagram, either LHS or RHS |
| key $1 \mid 9 \mid 4$ means 91 kg for team A and 94 kg for B | B1 (4) | Correct key or keys for their diagram/s, need both teams, at least one kg |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $LQ = 91$, $UQ = 109$, $IQ\ \text{range} = 18$ | B1 | Both quartiles correct |
| | B1$\checkmark$ (2) | Correct IQR ft wrong quartiles, $LQ < UQ$, not $12-4$ etc |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\Sigma x_{15} = 1399$ | M1 | Attempt at $\Sigma x_{15}$ for either team |
| $\Sigma x_{16} = 16 \times 93.9 = 1502.4$ | M1 | Mult 93.9 by 16 attempt |
| New wt $= 1502.4 - 1399 = 103\ (103.4)$ | A1 (3) | Correct answer |
---5 The weights, in kilograms, of the 15 rugby players in each of two teams, $A$ and $B$, are shown below.
\begin{center}
\begin{tabular}{ | l | l | l | r | r | r | r | r | r | r | r | r | r | r | r | r | }
\hline
Team $A$ & 97 & 98 & 104 & 84 & 100 & 109 & 115 & 99 & 122 & 82 & 116 & 96 & 84 & 107 & 91 \\
\hline
Team $B$ & 75 & 79 & 94 & 101 & 96 & 77 & 111 & 108 & 83 & 84 & 86 & 115 & 82 & 113 & 95 \\
\hline
\end{tabular}
\end{center}
(i) Represent the data by drawing a back-to-back stem-and-leaf diagram with team $A$ on the lefthand side of the diagram and team $B$ on the right-hand side.\\
(ii) Find the interquartile range of the weights of the players in team $A$.\\
(iii) A new player joins team $B$ as a substitute. The mean weight of the 16 players in team $B$ is now 93.9 kg . Find the weight of the new player.
\hfill \mbox{\textit{CAIE S1 2015 Q5 [9]}}