| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct stem-and-leaf then find median and quartiles |
| Difficulty | Easy -1.2 This is a straightforward data handling question requiring only routine procedures: ordering data, constructing a stem-and-leaf diagram, and finding the median/quartiles using standard position formulas. No problem-solving or conceptual insight is needed—just careful execution of basic statistical techniques taught early in S1. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 115 | 120 | 158 | 132 | 125 |
| 104 | 142 | 160 | 145 | 104 |
| 162 | 117 | 109 | 124 | 134 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Stem: 10\ | 4 4 9; 11\ | 5 7; 12\ |
| B1 | Correct leaves, must be sorted and in columns and give correct overall shape | |
| key: 10\ | 4 represents 104 | B1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| median \(= 125\), LQ \(= 115\), UQ \(= 145\) | B1 | Any 2 correct values seen |
| B1 [2] | Third correct value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Box plot drawn | B1 | Correct uniform scale from at least 110 to 160 with room for end points, and label or title |
| B1ft | Correct median and quartiles on diagram ft their values (must be box ends) | |
| B1 [3] | Correct whiskers, no line through box, touching box in the middle not the top or bottom |
## Question 5:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Stem: 10\|4 4 9; 11\|5 7; 12\|0 4 5; 13\|2 4; 14\|2 5; 15\|8; 16\|0 8 | B1 | Correct stem |
| | B1 | Correct leaves, must be sorted and in columns and give correct overall shape |
| key: 10\|4 represents 104 | B1 **[3]** | Key, must have vertical line in both |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| median $= 125$, LQ $= 115$, UQ $= 145$ | B1 | Any 2 correct values seen |
| | B1 **[2]** | Third correct value |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Box plot drawn | B1 | Correct uniform scale from at least 110 to 160 with room for end points, and label or title |
| | B1ft | Correct median and quartiles on diagram ft their values (must be box ends) |
| | B1 **[3]** | Correct whiskers, no line through box, touching box in the middle not the top or bottom |
---5 The pulse rates, in beats per minute, of a random sample of 15 small animals are shown in the following table.
\begin{center}
\begin{tabular}{ l l l l l }
115 & 120 & 158 & 132 & 125 \\
104 & 142 & 160 & 145 & 104 \\
162 & 117 & 109 & 124 & 134 \\
\end{tabular}
\end{center}
(i) Draw a stem-and-leaf diagram to represent the data.\\
(ii) Find the median and the quartiles.\\
(iii) On graph paper, using a scale of 2 cm to represent 10 beats per minute, draw a box-and-whisker plot of the data.
\hfill \mbox{\textit{CAIE S1 2008 Q5 [8]}}