| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | June |
| 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 -1.8 This is a routine data handling exercise requiring only mechanical construction of a stem-and-leaf diagram and basic statistical measures (median, IQR). No problem-solving or conceptual understanding is needed—just careful organization of given data and application of standard definitions. Significantly easier than average A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Bronlea | 21 | 45 | 6 | 33 | 27 | 3 | 32 | 14 | 28 | 24 | 13 | 17 | 25 | 22 |
| Rogate | 7 | 5 | 4 | 15 | 23 | 7 | 11 | 13 | 26 | 18 | 23 | 16 | 10 | 34 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct single stem | B1 | Correct single stem |
| Bronlea: \(6\ 3\ 0 \mid 4\ 5\ 7\ 7\) ordered leaves | B1 | Correct ordered leaves Bronlea |
| Rogate: \(7\ 4\ 3\ 1 \mid 0\ 1\ 3\ 5\ 6\ 8\) ordered leaves | B1 | Correct ordered leaves Rogate |
| \(8\ 7\ 5\ 4\ 2\ 1 \mid 2 \mid 3\ 3\ 6\) / \(3\ 2\ 3 \mid 4\) / \(5 \mid 4\) correct overall shape | B1 | Correct overall shape |
| Key: \(3\mid1\mid5\) represents 13 kph for Bronlea and 15 kph for Rogate | B1 [5] | Single key must have both towns and units consistent with their values |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median Bronlea \(= 23\) km per hour | B1 | Units not necessary |
| IQ range Rogate \(= 23 - 7 = 16\) | M1 A1 [3] | Subt their LQ \(<14\) from their UQ \(>14\) from Rogate leaf |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Rogate is less windy than Bronlea | B1 [1] | Not a comparison of a statistic but interpretation of information |
## Question 5:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct single stem | B1 | Correct single stem |
| Bronlea: $6\ 3\ 0 \mid 4\ 5\ 7\ 7$ ordered leaves | B1 | Correct ordered leaves Bronlea |
| Rogate: $7\ 4\ 3\ 1 \mid 0\ 1\ 3\ 5\ 6\ 8$ ordered leaves | B1 | Correct ordered leaves Rogate |
| $8\ 7\ 5\ 4\ 2\ 1 \mid 2 \mid 3\ 3\ 6$ / $3\ 2\ 3 \mid 4$ / $5 \mid 4$ correct overall shape | B1 | Correct overall shape |
| Key: $3\mid1\mid5$ represents 13 kph for Bronlea and 15 kph for Rogate | B1 [5] | Single key must have both towns and units consistent with their values |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median Bronlea $= 23$ km per hour | B1 | Units not necessary |
| IQ range Rogate $= 23 - 7 = 16$ | M1 A1 [3] | Subt their LQ $<14$ from their UQ $>14$ from Rogate leaf |
### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Rogate is less windy than Bronlea | B1 [1] | Not a comparison of a statistic but interpretation of information |
---5 The following are the maximum daily wind speeds in kilometres per hour for the first two weeks in April for two towns, Bronlea and Rogate.
\begin{center}
\begin{tabular}{ | l | r | r | r | r | r | r | r | r | r | r | r | r | r | r | }
\hline
Bronlea & 21 & 45 & 6 & 33 & 27 & 3 & 32 & 14 & 28 & 24 & 13 & 17 & 25 & 22 \\
\hline
Rogate & 7 & 5 & 4 & 15 & 23 & 7 & 11 & 13 & 26 & 18 & 23 & 16 & 10 & 34 \\
\hline
\end{tabular}
\end{center}
(i) Draw a back-to-back stem-and-leaf diagram to represent this information.\\
(ii) Write down the median of the maximum wind speeds for Bronlea and find the interquartile range for Rogate.\\
(iii) Use your diagram to make one comparison between the maximum wind speeds in the two towns.
\hfill \mbox{\textit{CAIE S1 2016 Q5 [9]}}