Victorian Curriculum Year 10A - 2020 Edition
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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:

0
2
4
6
8
10
12
14
16
18
20
score
  1. Complete the table for the given data:

    Minimum $\editable{}$
    Lower Quartile $\editable{}$
    Median $\editable{}$
    Upper Quartile $\editable{}$
    Maximum $\editable{}$

Question 2

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

Minimum $10$10
Lower quartile $20$20
Median $40$40
Upper quartile $55$55
Maximum $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.

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