| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Interpret or analyse given back-to-back stem-and-leaf |
| Difficulty | Moderate -0.8 This is a straightforward stem-and-leaf interpretation question requiring basic statistical skills: reading ordered data to find median and quartiles (standard procedure for n=39), then drawing box plots. The back-to-back format adds minimal complexity, and part (ii) is purely mechanical plotting with male statistics already provided. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Females | Males | |||||||||||||||||||
| (4) | \multirow{7}{*}{9} | 5 | 2 | 0 | 0 | 20 | 3 | |||||||||||||
| (9) | 8 | 8 | 7 | 6 | 4 | 0 | 0 | 0 | 21 | 0 | 0 | 7 | ||||||||
| (8) | \multirow{5}{*}{} | 8 | 7 | 5 | 3 | 3 | 1 | 0 | 0 | 22 | 0 | 0 | 4 | 5 | 6 | 6 | ||||
| (6) | \multirow{4}{*}{} | 6 | 4 | 2 | 1 | 0 | 0 | 23 | 0 | 0 | 2 | 3 | 3 | 5 | 6 | 7 | 7 | |||
| (6) | 7 | 5 | 4 | 0 | 0 | 0 | 24 | 0 | 1 | 1 | 2 | 5 | 5 | 6 | 8 | 8 | 9 | |||
| (4) | 9 | 5 | 0 | 0 | 25 | 3 | 4 | 5 | 7 | 7 | 8 | 9 | ||||||||
| (2) | 5 | 0 | 26 | 0 | 4 | 6 | ||||||||||||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| females: med \$22 700 | B1 | Any 2 correct |
| LQ \\(21700, UQ \\)24 000 | B1 [2] | All correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct box plot for males drawn | B1 | Uniform scale and labels must see Salary, \$000 |
| Correct graph for females fitting their quartiles. Line not through box | B1 | Correct graph for females ft their quartiles |
| Correct graph for males | B1 [3] |
## Question 3:
### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| females: med \$22 700 | B1 | Any 2 correct |
| LQ \$21700, UQ \$24 000 | B1 **[2]** | All correct |
### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct box plot for males drawn | B1 | Uniform scale and labels must see Salary, \$000 |
| Correct graph for females fitting their quartiles. Line not through box | B1 | Correct graph for females ft their quartiles |
| Correct graph for males | B1 **[3]** | |
---3 The following back-to-back stem-and-leaf diagram shows the annual salaries of a group of 39 females and 39 males.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
& \multicolumn{9}{|c|}{Females} & & \multicolumn{10}{|c|}{Males} \\
\hline
(4) & \multirow{7}{*}{9} & & & & & 5 & 2 & 0 & 0 & 20 & 3 & & & & & & & & & \\
\hline
(9) & & 8 & 8 & 7 & 6 & 4 & 0 & 0 & 0 & 21 & 0 & 0 & 7 & & & & & & & \\
\hline
(8) & \multirow{5}{*}{} & 8 & 7 & 5 & 3 & 3 & 1 & 0 & 0 & 22 & 0 & 0 & 4 & 5 & 6 & 6 & & & & \\
\hline
(6) & \multicolumn{2}{|c|}{\multirow{4}{*}{}} & & 6 & 4 & 2 & 1 & 0 & 0 & 23 & 0 & 0 & 2 & 3 & 3 & 5 & 6 & 7 & 7 & \\
\hline
(6) & & & & 7 & 5 & 4 & 0 & 0 & 0 & 24 & 0 & 1 & 1 & 2 & 5 & 5 & 6 & 8 & 8 & 9 \\
\hline
(4) & & & & & & 9 & 5 & 0 & 0 & 25 & 3 & 4 & 5 & 7 & 7 & 8 & 9 & & & \\
\hline
(2) & & & & & & & & 5 & 0 & 26 & 0 & 4 & 6 & & & & & & & \\
\hline
\end{tabular}
\end{center}
Key: 2 | 20 | 3 means \$20200 for females and \$20300 for males.\\
(i) Find the median and the quartiles of the females' salaries.
You are given that the median salary of the males is $\$ 24000$, the lower quartile is $\$ 22600$ and the upper quartile is $\$ 25300$.\\
(ii) Represent the data by means of a pair of box-and-whisker plots in a single diagram on graph paper.
\hfill \mbox{\textit{CAIE S1 2013 Q3 [5]}}