# 11.02 Box plots

Lesson

### Box plots

Box plots (also known as box-and-whisker plots) are a way of showing the five-number summary for a data set. The five number summary consists of the following five statistics:

 Minimum $17$17 Lower Quartile $52$52 Median $69$69 Upper Quartile $87$87 Maximum $100$100

The box plot below shows a nice summary of all this information:

As you can see the box plot consists of a number line, a rectangle with a line inside (the box), and 2 horizontal lines (the whiskers). The box represents the middle $50%$50% of the scores and its size tells us the interquartile range.

#### Worked example

##### Example 2

Using the box-and-whisker plot above:

a) what percentage of scores lie between:

$10.9$10.9 and $11.2$11.2

$10.8$10.8 and $10.9$10.9

$11.1$11.1 and $11.3$11.3

$10.9$10.9 and $11.3$11.3

$10.8$10.8 and $11.2$11.2

Think: For these five questions, think about how many quartiles are in that range. Remember that one quartile represents $25%$25% of the data set.

Do:

$50%$50% of the scores lie between Q1 to Q3.

$25%$25% of the scores lie between the lowest score and Q1.

$50%$50% of the scores lie between the median and the highest score.

$75%$75% of the scores lie between Q2 and the highest score.

$75%$75% of the scores lie between the lowest score and Q3.

b) In which quartile (or quartiles) is the data the most spread out?

Think: Which quartile takes up the longest space on the graph?

Do: The second quartile is the most spread out.

##### Example 3

Using the information in the table, create a box plot to represent this data:

 Minimum $5$5 Lower Quartile $25$25 Median $40$40 Upper Quartile $45$45 Maximum $65$65

Think: Where do each of these values sit on a box and whisker plot?

Do: Here is our graph. Notice how the values in our table correspond to particular places on the box-and-whisker plot.

Summary

Box plots are a graphical representation showing the five-number summary for a data set.

 Minimum $17$17 Lower Quartile $52$52 Median $69$69 Upper Quartile $87$87 Maximum $100$100

#### Practice questions

##### Question 1

For the box plot shown below, find each of the following:

 02468101214161820score
1. Complete the table for the given data:

Minimum $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

##### Question 2

Create a box plot to represent the data in the table below.

Minimum $10$10 $20$20 $40$40 $55$55 $75$75
1. 0
10
20
30
40
50
60
70
80
90
100

### Outcomes

#### VCMSP350

Construct and interpret box plots and use them to compare data sets.