11.02 Box plots
Consider the following box plot below and the corresponding five number summary:
Fill in the missing numbers on the box plot.
| Minimum | 20 |
|---|---|
| Lower Quartile | 28 |
| Median | 36 |
| Upper Quartile | 42 |
| Maximum | 52 |
| Minimum | 16 |
|---|---|
| Lower Quartile | 33 |
| Median | 47 |
| Upper Quartile | 61 |
| Maximum | 71 |
| Minimum | 26 |
|---|---|
| Lower Quartile | 33 |
| Median | 41 |
| Upper Quartile | 44 |
| Maximum | 45 |
For each of the following box plots, construct a five number summary:
Create a box plot to represent the information in the following tables:
| Minimum | 5 |
|---|---|
| Lower Quartile | 25 |
| Median | 40 |
| Upper Quartile | 55 |
| Maximum | 65 |
| Minimum | 10 |
|---|---|
| Lower quartile | 20 |
| Median | 40 |
| Upper quartile | 55 |
| Maximum | 75 |
| Minimum | 10 |
|---|---|
| Lower quartile | 20 |
| Median | 40 |
| Upper quartile | 55 |
| Maximum | 75 |
| Minimum | 30 |
|---|---|
| Lower quartile | 31 |
| Median | 47 |
| Upper quartile | 53 |
| Maximum | 58 |
For each of the following data sets:
Construct the five number summary.
Draw a box plot.
14, 15, 20, 21, 23, 24, 27
21, 25, 29, 31, 32, 34, 39, 40
40, 12, 8, 20, 12, 28, 48, 36, 60
28, 4, 40, 16, 20, 48, 20, 44, 56
42, 43, 48, 54, 59, 51, 53, 50, 57, 45
60, 66, 67, 68, 69, 72, 73, 76, 77, 78, 86
| Leaf | |
|---|---|
| 4 | 2\ 3\ 5\ 8\ 9 |
| 5 | 0\ 2\ 3\ 4\ 6\ 7 |
| 6 | 1\ 2\ 4\ 5 |
Key: 1 | 2 = 12
| Leaf | |
|---|---|
| 2 | 0\ 4\ 4\ 5\ 7\ 7 |
| 3 | 1\ 2\ 3\ 5\ 5 |
| 4 | 3\ 3\ 5\ 9 |
Key: 1 | 2 = 12
Consider the box plot shown:
State the percentage of scores that lie between each of the following values:
7 and 15
1 and 7
9 and 19
7 and 19
1 and 15
In which quartile is the data the least spread out?
A geography teacher has marked a set of tests. She wants to represent the results in a box plot. She has already sorted her data and created the following table:
Create a box plot to represent the data in the table.
| Minimum | 4 |
|---|---|
| Lower Quartile | 10 |
| Median | 22 |
| Upper Quartile | 26 |
| Maximum | 38 |
A mathematics teacher has marked a set of tests. She then sorted her data and created the following table:
Create a box plot to represent the data in the table.
| Minimum | 2 |
|---|---|
| Lower quartile | 10 |
| Median | 16 |
| Upper quartile | 22 |
| Maximum | 30 |
The box plot shows the age at which a group of people got their driving licences:
What is the oldest age?
What is the youngest age?
What percentage of people were aged from 18 to 22?
The middle 50\% of responders were within how many years of one another?
In which quartile are the ages least spread out?
The bottom 50\% of responders were within how many years of one another?
Construct a box plot for the following data set:
Range = 14
Lowest score = 2
IQR = 8
25\% of scores are below 4
50\% of scores are above 8
The test scores of 11 students in Science and Music are listed below:
Science: 52, 59, 87, 66, 74, 76, 73, 63, 91, 86, 82
-
Music: 87, 63, 74, 55, 74, 82, 66, 61, 88, 76, 84
Construct a box plot for the Science scores.
Construct a box plot for the Music scores.
Which subject had the highest score?
The marks in an end-of-year exam for a class of students are given below:
52,\, 95,\, 80,\, 56,\, 59,\, 80,\, 86,\, 77,\, 80,\, 81,\, 78,\, 64,\, 84,\, 66,\, 96,\, 90
Construct a box plot for the data.
Calculate the interquartile range.
What percentage of marks lie in the range 85 to 96?
Which values do the lowest 75\% of scores lie between?
In training, a fighter pilot measures the number of seconds he blacks out over a number of flights. He constructs the following box and whisker plot:
As long as the pilot is not unconscious for more than 7 seconds, he will be safe to fly.
The pilot concludes that he is safe to fly all the time. Explain why his conclusion is incorrect.