| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| 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 -2.0 This is a routine data handling exercise requiring only basic skills: organizing data into a stem-and-leaf diagram and finding standard summary statistics from ordered data. These are fundamental, procedural tasks with no problem-solving or conceptual challenge beyond recall of definitions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 17 | 5 | 2 | 23 | 16 | 31 | 8 |
| 22 | 14 | 25 | 35 | 17 | 27 | 12 |
| 6 | 23 | 19 | 21 | 23 | 8 | 26 |
| Answer | Marks | Guidance |
|---|---|---|
| Key: 1 | 2 represents 12 people | |
| 0 | 2 5 6 8 8 | |
| 1 | 2 4 6 7 7 9 | |
| 2 | 1 2 3 3 3 5 6 7 | |
| 3 | 1 5 | |
| B1, B1, B1 | Correct stem; Correct leaves must be sorted and accurate; Key; must have people o.e. | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| median = 19 people, LQ = 10, UQ = 24, IQ range = 24 − 10 = 14 people | B1, B1, B1 ft | Correct median; Correct quartiles; Fit their quartiles |
| Answer | Marks | Guidance |
|---|---|---|
| median because mode could be any number which is duplicated more than twice | B1 | Correct answer must say something about the mode being not much use or another sensible reason |
**(i) Stem-and-leaf diagram:**
| | Key: 1 | 2 represents 12 people |
|---|---|---|
| 0 | 2 5 6 8 8 | |
| 1 | 2 4 6 7 7 9 | |
| 2 | 1 2 3 3 3 5 6 7 | |
| 3 | 1 5 | |
| B1, B1, B1 | Correct stem; Correct leaves must be sorted and accurate; Key; must have people o.e. | **[3]**
**(ii) Median and quartiles:**
median = 19 people, LQ = 10, UQ = 24, IQ range = 24 − 10 = 14 people | B1, B1, B1 ft | Correct median; Correct quartiles; Fit their quartiles | **[3]**
**(iii) Reason for median over mode:**
median because mode could be any number which is duplicated more than twice | B1 | Correct answer must say something about the mode being not much use or another sensible reason | **[1]**
---2 The numbers of people travelling on a certain bus at different times of the day are as follows.
\begin{center}
\begin{tabular}{ r r r r r r r }
17 & 5 & 2 & 23 & 16 & 31 & 8 \\
22 & 14 & 25 & 35 & 17 & 27 & 12 \\
6 & 23 & 19 & 21 & 23 & 8 & 26 \\
\end{tabular}
\end{center}
(i) Draw a stem-and-leaf diagram to illustrate the information given above.\\
(ii) Find the median, the lower quartile, the upper quartile and the interquartile range.\\
(iii) State, in this case, which of the median and mode is preferable as a measure of central tendency, and why.
\hfill \mbox{\textit{CAIE S1 2010 Q2 [7]}}