Exam-Style Problems
⬅ Back to SubchapterJune 2013 p61 q3
The following back-to-back stem-and-leaf diagram shows the annual salaries of a group of 39 females and 39 males.
| Females | Males | |||
|---|---|---|---|---|
| (4) | 5 2 0 0 | 20 | 3 | (1) |
| (9) | 9 8 8 7 6 4 0 0 0 | 21 | 0 0 7 | (3) |
| (8) | 8 7 5 3 3 1 0 0 | 22 | 0 0 0 4 5 6 6 | (6) |
| (6) | 6 4 2 1 0 0 | 23 | 0 0 2 3 3 5 6 7 7 | (9) |
| (6) | 7 5 4 0 0 0 | 24 | 0 1 1 2 5 5 6 8 8 9 | (10) |
| (4) | 9 5 0 0 | 25 | 3 4 5 7 7 8 9 | (7) |
| (2) | 5 0 | 26 | 0 4 6 | (3) |
Key: 2 | 20 | 3 means $20 200 for females and $20 300 for males.
(i) Find the median and the quartiles of the females’ salaries.
You are given that the median salary of the males is \($24 000\), the lower quartile is \($22 600\) and the upper quartile is \($25 300.\)
(ii) Represent the data by means of a pair of box-and-whisker plots in a single diagram on graph paper.
June 2012 p62 q4
The back-to-back stem-and-leaf diagram shows the values taken by two variables A and B.
| A | B | |||
|---|---|---|---|---|
| (3) | 3 1 0 | 15 | 1 3 3 5 | (4) |
| (2) | 4 1 | 16 | 2 2 3 4 4 5 7 7 8 | (10) |
| (3) | 8 3 3 | 17 | 0 1 3 3 3 4 6 6 7 9 9 | (11) |
| (12) | 9 8 8 6 5 5 4 3 2 1 1 0 | 18 | 2 4 7 | (3) |
| (8) | 9 9 8 8 6 5 4 2 | 19 | 1 5 | (2) |
| (5) | 9 8 7 1 0 | 20 | 4 | (1) |
Key: \(4 \mid 16 \mid 7\) means \(A = 0.164\) and \(B = 0.167\).
- Find the median and the interquartile range for variable A.
- You are given that, for variable B, the median is 0.171, the upper quartile is 0.179 and the lower quartile is 0.164. Draw box-and-whisker plots for A and B in a single diagram on graph paper.
Nov 2011 p61 q4
The marks of the pupils in a certain class in a History examination are as follows.
28, 33, 55, 38, 42, 39, 27, 48, 51, 37, 57, 49, 33
The marks of the pupils in a Physics examination are summarised as follows.
Lower quartile: 28, Median: 39, Upper quartile: 67. The lowest mark was 17 and the highest mark was 74.
- Draw box-and-whisker plots in a single diagram on graph paper to illustrate the marks for History and Physics.
- State one difference, which can be seen from the diagram, between the marks for History and Physics.
June 2010 p63 q6
The lengths of some insects of the same type from two countries, X and Y, were measured. The stem-and-leaf diagram shows the results.
| Country X | Country Y | |||
|---|---|---|---|---|
| (10) | 9 7 6 6 6 4 4 3 2 0 | 80 | ||
| (18) | 8 8 7 7 6 6 5 5 5 4 4 3 3 2 2 0 | 81 | 1 1 2 2 3 3 3 5 5 6 7 8 9 | (13) |
| (16) | 9 9 9 8 8 7 7 6 5 5 3 2 1 1 0 0 | 82 | 0 0 1 2 3 3 q 4 5 6 6 7 8 8 | (15) |
| (16) | 8 7 6 5 5 5 3 3 2 2 1 1 1 0 0 | 83 | 0 1 2 2 4 4 4 5 5 6 7 7 7 8 9 | (17) |
| (11) | 8 7 6 5 5 4 4 3 3 1 1 | 84 | 0 1 2 4 4 5 5 6 7 7 7 8 9 | (15) |
| 85 | 1 2 r 3 3 5 5 6 7 8 8 | (12) | ||
| 86 | 0 1 2 2 3 5 5 8 9 9 | (11) |
Key: 5 | 81 | 3 means an insect from country X has length 0.815 cm and an insect from country Y has length 0.813 cm.
- Find the median and interquartile range of the lengths of the insects from country X.
- The interquartile range of the lengths of the insects from country Y is 0.028 cm. Find the values of \(q\) and \(r\).
- Represent the data by means of a pair of box-and-whisker plots in a single diagram on graph paper.
- Compare the lengths of the insects from the two countries.
Nov 2009 p61 q4
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.
| 3 | 6 9 9 | (4) |
| 4 | 6 7 | (2) |
| 5 | 0 1 2 2 | (4) |
| 6 | 0 1 1 2 3 4 4 4 5 5 6 6 6 7 8 9 | (20) |
| 7 | 1 1 3 3 3 5 6 7 8 9 9 | (12) |
| 8 | 0 2 4 5 5 6 8 | (7) |
| 9 | 0 1 2 4 4 4 5 5 6 7 7 8 8 9 9 | (18) |
Key: \( 3 \mid 6 \) represents 36 books.
- Find the number of shelves in this section of the library.
- 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.
| 2 | 1 2 2 3 3 4 5 6 6 6 7 9 | (13) |
| 3 | 0 1 1 2 3 4 5 6 6 7 7 8 8 | (15) |
| 4 | 2 2 3 5 7 8 9 | (8) |
Key: \( 3 \mid 6 \) represents 36 books.
- 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.
