Exam-Style Problems
⬅ Back to SubchapterJune 2023 p52 q3
The following back-to-back stem-and-leaf diagram represents the monthly salaries, in dollars, of 27 employees at each of two companies, A and B.
| Company A | Company B | |
|---|---|---|
| 5 4 1 1 0 | 25 | 4 4 5 6 6 7 |
| 9 9 8 7 2 0 | 26 | 0 1 3 5 7 9 9 |
| 8 6 4 2 1 0 | 27 | 1 3 4 6 6 8 8 |
| 6 5 4 2 0 | 28 | 0 1 2 2 2 |
| 9 8 5 | 29 | |
| 1 | 30 | 9 |
Key: 1 | 27 | 6 means $2710 for company A and $2760 for company B.
(a) Find the median and the interquartile range of the monthly salaries of employees in company A.
The lower quartile, median and upper quartile for company B are $2600, $2690 and $2780 respectively.
(b) Draw two box-and-whisker plots in a single diagram to represent the information for the salaries of employees at companies A and B.
(c) Comment on whether the mean would be a more appropriate measure than the median for comparing the given information for the two companies.
June 2016 p63 q2
A group of children played a computer game which measured their time in seconds to perform a certain task. A summary of the times taken by girls and boys in the group is shown below.
| Minimum | Lower quartile | Median | Upper quartile | Maximum | |
|---|---|---|---|---|---|
| Girls | 5 | 5.5 | 7 | 9 | 13 |
| Boys | 4 | 6 | 8.5 | 11 | 16 |
- On graph paper, draw two box-and-whisker plots in a single diagram to illustrate the times taken by girls and boys to perform this task.
- State two comparisons of the times taken by girls and boys.
Nov 2014 p63 q4
A random sample of 25 people recorded the number of glasses of water they drank in a particular week. The results are shown below.
23, 19, 32, 14, 25, 22, 26, 36, 45, 42, 47, 28, 17, 38, 15, 46, 18, 26, 22, 41, 19, 21, 28, 24, 30
On graph paper draw a box-and-whisker plot to represent the data.
Nov 2014 p61 q4
The following back-to-back stem-and-leaf diagram shows the times to load an application on 61 smartphones of type A and 43 smartphones of type B.
| Type A | Type B | |||
|---|---|---|---|---|
| (7) | 9 7 6 6 4 3 3 | 2 | 1 3 5 8 | (4) |
| (7) | 5 5 4 4 2 2 2 | 3 | 0 4 4 5 6 6 6 7 8 9 | (12) |
| (13) | 9 9 8 8 8 7 6 4 3 2 2 0 | 4 | 0 1 1 2 3 6 8 8 9 9 | (10) |
| (9) | 6 5 5 4 3 2 1 1 0 | 5 | 2 5 6 6 9 | (5) |
| (4) | 9 7 3 0 | 6 | 1 3 8 9 | (4) |
| (6) | 8 7 4 4 1 0 | 7 | 5 7 | (2) |
| (10) | 7 6 6 6 5 3 2 1 0 | 8 | 1 2 4 4 | (4) |
| (5) | 8 6 5 5 5 | 9 | 0 6 | (2) |
Key: 3 | 2 | 1 means 0.23 seconds for type A and 0.21 seconds for type B.
- Find the median and quartiles for smartphones of type A.
- Represent the data by drawing a pair of box-and-whisker plots in a single diagram on graph paper.
- Compare the loading times for these two types of smartphone.
Nov 2013 p61 q4
The following are the house prices in thousands of dollars, arranged in ascending order, for 51 houses from a certain area.
| 253 | 270 | 310 | 354 | 386 | 428 | 433 | 468 | 472 | 477 | 485 | 520 | 520 | 524 | 526 | 531 | 535 |
| 536 | 538 | 541 | 543 | 546 | 548 | 549 | 551 | 554 | 572 | 583 | 590 | 605 | 614 | 638 | 649 | 652 |
| 666 | 670 | 682 | 684 | 690 | 710 | 725 | 726 | 731 | 734 | 745 | 760 | 800 | 854 | 863 | 957 | 986 |
- Draw a box-and-whisker plot to represent the data.
- For the above data, give the prices of the expensive houses.
- Give one disadvantage of using a box-and-whisker plot rather than a stem-and-leaf diagram to represent this set of data.
An expensive house is defined as a house which has a price that is more than 1.5 times the interquartile range above the upper quartile.
