| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2022 |
| 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 straightforward data handling question requiring basic statistical skills: organizing data into a stem-and-leaf diagram, finding median and quartiles from ordered data (n=11, so positions are clear), and making simple comparisons. All techniques are routine recall with no problem-solving or conceptual challenges. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Lions | 178 | 186 | 181 | 187 | 179 | 190 | 189 | 190 | 180 | 169 | 196 |
| Tigers | 194 | 179 | 187 | 190 | 183 | 201 | 184 | 180 | 195 | 191 | 197 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct stem (16,17,18,19,20) | B1 | Correct stem can be upside down, ignore extra values (not in reverse) |
| Lions leaves in order from right to left, lined up vertically | B1 | Correct Lions labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation |
| Tigers leaves in order, lined up vertically | B1 | Correct Tigers labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation. If correct data for Lions and Tigers transposed, treat as single error in Lions and condone in Tigers |
| Key: \(1\ | 18\ | 3\) means 181 cm for Lions and 183 cm for Tigers |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 186\) cm | B1 | |
| \([\text{UQ} = 190\ \text{cm},\ \text{LQ} = 179\ \text{cm}]\) \(\text{IQR} = 190 - 179\) | M1 | \(189 \leqslant \text{UQ} \leqslant 190 - 178 \leqslant \text{LQ} \leqslant 180\) |
| \(11\ [\text{cm}]\) | A1 | WWW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Tigers are (generally) taller | B1 | Comparison about central tendency in context |
| Heights of Tigers are slightly less consistent than heights of Lions | B1 | Comparison about spread in context. (Condone 'similar spread' in context.) |
## Question 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct stem (16,17,18,19,20) | B1 | Correct stem can be upside down, ignore extra values (not in reverse) |
| Lions leaves in order from right to left, lined up vertically | B1 | Correct Lions labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation |
| Tigers leaves in order, lined up vertically | B1 | Correct Tigers labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation. If correct data for Lions and Tigers transposed, treat as single error in Lions and condone in Tigers |
| Key: $1\|18\|3$ means 181 cm for Lions and 183 cm for Tigers | B1 | Correct single key for their diagram, need both teams identified and 'cm' stated at least once. **SC** If 2 separate diagrams drawn, **SC B1** if both keys meet criteria (Max B1, B0, B0, B1) |
---
## Question 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 186$ cm | B1 | |
| $[\text{UQ} = 190\ \text{cm},\ \text{LQ} = 179\ \text{cm}]$ $\text{IQR} = 190 - 179$ | M1 | $189 \leqslant \text{UQ} \leqslant 190 - 178 \leqslant \text{LQ} \leqslant 180$ |
| $11\ [\text{cm}]$ | A1 | WWW |
---
## Question 3(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Tigers are (generally) taller | B1 | Comparison about central tendency in context |
| Heights of Tigers are slightly less consistent than heights of Lions | B1 | Comparison about spread in context. (Condone 'similar spread' in context.) |
---3 The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of their first team squads are given in the table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | l | l | l | l | }
\hline
Lions & 178 & 186 & 181 & 187 & 179 & 190 & 189 & 190 & 180 & 169 & 196 \\
\hline
Tigers & 194 & 179 & 187 & 190 & 183 & 201 & 184 & 180 & 195 & 191 & 197 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a back-to-back stem-and-leaf diagram to represent this information, with the Lions on the left.
\item Find the median and the interquartile range of the heights of the Lions first team squad.\\
It is given that for the Tigers, the lower quartile is 183 cm , the median is 190 cm and the upper quartile is 195 cm .
\item Make two comparisons between the heights of the players in the Lions first team squad and the heights of the players in the Tigers first team squad.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2022 Q3 [9]}}