| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.2 This is a straightforward stem-and-leaf diagram question requiring basic counting to find median/quartiles and simple algebra to find x using the given IQR. The skills are purely procedural: counting positions (n=31, so median is 16th value), identifying quartile positions, and solving IQR = Q3 - Q1 = 19. No conceptual depth or problem-solving insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 0 | 0 | 1 | 5 | 6 | |||||
| 1 | 1 | 3 | 5 | 6 | 6 | 8 | |||
| 2 | 1 | 1 | 2 | 3 | 4 | 4 | 4 | 8 | 9 |
| 3 | 1 | 2 | 2 | 2 | \(x\) | 8 | 9 | ||
| 4 | 2 | 5 | 6 | 7 | 9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| median = \(16^{\text{th}}\) along = 24 | B1 | |
| \(LQ = 16\) not 15.5 | B1 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(UQ = LQ + 19 = 35\) | M1 | For adding 19 to their LQ in whatever form |
| \(x = 5\) | A1 2 | Must be 5 not 35. c.w.o. |
## Question 1:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| median = $16^{\text{th}}$ along = 24 | B1 | |
| $LQ = 16$ not 15.5 | B1 **2** | |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $UQ = LQ + 19 = 35$ | M1 | For adding 19 to their LQ in whatever form |
| $x = 5$ | A1 **2** | Must be 5 not 35. c.w.o. |
---1 The stem-and-leaf diagram below represents data collected for the number of hits on an internet site on each day in March 2007. There is one missing value, denoted by $x$.
\begin{center}
\begin{tabular}{ l | l l l l l l l l l }
0 & 0 & 1 & 5 & 6 & & & & & \\
1 & 1 & 3 & 5 & 6 & 6 & 8 & & & \\
2 & 1 & 1 & 2 & 3 & 4 & 4 & 4 & 8 & 9 \\
3 & 1 & 2 & 2 & 2 & $x$ & 8 & 9 & & \\
4 & 2 & 5 & 6 & 7 & 9 & & & & \\
\end{tabular}
\end{center}
Key: 1 | 5 represents 15 hits\\
(i) Find the median and lower quartile for the number of hits each day.\\
(ii) The interquartile range is 19 . Find the value of $x$.
\hfill \mbox{\textit{CAIE S1 2008 Q1 [4]}}