| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 7 |
| 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 -1.3 This question requires only basic counting and reading values from stem-and-leaf diagrams to find median and quartiles. The tasks are entirely procedural: count data points, identify positions for quartiles, and make a simple comparison. No calculation complexity or conceptual insight is needed beyond understanding what a stem-and-leaf diagram represents. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 3 | 3699 | |||
| 4 | 67 | |||
| 5 | 0122 | |||
| 6 | 00112344444556667889 | |||
| 7 | 113335667899 | |||
| 8 | 0245568 | |||
| 9 | 001244445567788999 |
| 2 | 12222334566679 | \(( 13 )\) | |
| 3 | 01112334456677788 | \(( 15 )\) | |
| 4 | 223357789 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(67\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(LQ=64\), \(Med=73\), \(UQ=90\) | M1 | Attempt to find all 3 quartiles can be implied |
| [Box-and-whisker diagram] | B1 | Correct end whiskers (not dots or boxes), not through box, must look accurate |
| B1 | Correct median line in box must look accurate | |
| B1 | Correct box ends must look accurate | |
| Scale from 30 to 100, labelled 'books' | B1 [5] | Correct uniform scale from at least 33 to 99, and label 'books' oe can be seen in title or scale |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Books are fatter/wider, or standard deviation/IQ range of the number of books per shelf is less | B1 [1] | Any sensible comment about width of books or s.d./IQ range not mean/median |
# Question 4:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $67$ | B1 **[1]** | |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $LQ=64$, $Med=73$, $UQ=90$ | M1 | Attempt to find all 3 quartiles can be implied |
| [Box-and-whisker diagram] | B1 | Correct end whiskers (not dots or boxes), not through box, must look accurate |
| | B1 | Correct median line in box must look accurate |
| | B1 | Correct box ends must look accurate |
| Scale from 30 to 100, labelled 'books' | B1 **[5]** | Correct uniform scale from at least 33 to 99, and label 'books' oe can be seen in title or scale |
## Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Books are fatter/wider, or standard deviation/IQ range of the number of books per shelf is less | B1 **[1]** | Any sensible comment about width of books or s.d./IQ range not mean/median |
---4 A library has many identical shelves. All the shelves are full and the numbers of books on each shelf in a certain section are summarised by the following stem-and-leaf diagram.
\begin{center}
\begin{tabular}{ l | l l l l }
3 & 3699 & & & \\
4 & 67 & & & \\
5 & 0122 & & & \\
6 & 00112344444556667889 & & & \\
7 & 113335667899 & & & \\
8 & 0245568 & & & \\
9 & 001244445567788999 & & & \\
\end{tabular}
\end{center}
Key: 3 | 6 represents 36 books\\
(i) Find the number of shelves in this section of the library.\\
(ii) Draw a box-and-whisker plot to represent the data.
In another section all the shelves are full and the numbers of books on each shelf are summarised by the following stem-and-leaf diagram.
\begin{center}
\begin{tabular}{ l | l l l l l l l l }
2 & 12222334566679 & $( 13 )$ & \\
3 & 01112334456677788 & $( 15 )$ & \\
4 & 223357789 & & \\
\end{tabular}
\end{center}
Key: 3 | 6 represents 36 books\\
(iii) There are fewer books in this section than in the previous section. State one other difference between the books in this section and the books in the previous section.
\hfill \mbox{\textit{CAIE S1 2009 Q4 [7]}}