| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Box plot construction or interpretation |
| Difficulty | Easy -1.3 This question requires only basic recall of box plot definitions (IQR = UQ - LQ) and straightforward plotting with a given scale. Part (i) is a single arithmetic step, and part (ii) is mechanical plotting of five given values with no interpretation or problem-solving required. |
| Spec | 2.02f Measures of average and spread2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | Subtracting IQR from UQ | |
| A1 | 2 marks | Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| B1 | Correct whiskers (accept hour decimals or minutes) | |
| B1 | Correct median line, can be broken or extended | |
| B1 ft | Correct UQ and LQ ft on their (i), box ends | |
| B1 | 4 marks | Correct uniform scale label hours or minutes, could be heading or key |
**(i)** $\text{LQ} = 4 \text{ hr } 42 \text{ min} - 3 \text{ hr } 48 \text{ min} = 54 \text{ min}$ $(0.9 \text{ hours})$
| M1 | Subtracting IQR from UQ |
| A1 | 2 marks | Correct answer |
**(ii)** Box plot with correct whiskers, median line, and scale
| B1 | Correct whiskers (accept hour decimals or minutes) |
| B1 | Correct median line, can be broken or extended |
| B1 ft | Correct UQ and LQ ft on their (i), box ends |
| B1 | 4 marks | Correct uniform scale label hours or minutes, could be heading or key |
---3 In a survey, people were asked how long they took to travel to and from work, on average. The median time was 3 hours 36 minutes, the upper quartile was 4 hours 42 minutes and the interquartile range was 3 hours 48 minutes. The longest time taken was 5 hours 12 minutes and the shortest time was 30 minutes.\\
(i) Find the lower quartile.\\
(ii) Represent the information by a box-and-whisker plot, using a scale of 2 cm to represent 60 minutes.
\hfill \mbox{\textit{CAIE S1 2006 Q3 [6]}}