Comparative displays | Year 6

01 / LEARN

The idea, step by step

Compare like with like

A frequency tells how many observations have a value or fall in a category. In a grouped column graph, read the key first, then compare bars above the same horizontal label. A bar height of 4 means four students, not four books.

Use the table to check the graph. Here each class has ten students, so counts can be compared directly. If class sizes differed, we would need to account for that difference before saying one class had a greater proportion.

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

Describe a comparison with evidence

Choose a question before comparing. To compare students who finished at least two books, combine the frequencies for 2 and 3 books in each class. Do not compare one selected bar and ignore the rest.

A useful sentence names both groups, the feature and the evidence: seven of ten Class B students finished at least two books, compared with four of ten in Class A. This describes these practice data; it does not tell us why the classes differ.

A common trap

The tallest bar tells us the total number of books.

Instead: Read the vertical-axis label: these bar heights count students at each number of books.

02 / WORKED EXAMPLES

See the thinking

Example 1

Compare a single value

Using the supplied table, how many more Class B students than Class A students finished exactly three books?

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

At 3 books, Class B has 3 students and Class A has 1.
Subtract the frequencies: $3 - 1 = 2$ .

2 more students.

Example 2

Combine categories

Using the table, compare the numbers who finished at least two books.

Practice data: books finished during one week by ten students in each class
Books finished	Class A frequency	Class B frequency
0	2	1
1	4	2
2	3	4
3	1	3

Class A: $3 + 1 = 4$ students.
Class B: $4 + 3 = 7$ students.
Both groups contain 10 students, so Class B has 3 more students in this category.

Class B: 7 of 10; Class A: 4 of 10.

Check your understanding

In the supplied data, which class has more students who finished no books?

Show answer

Class A.

The frequencies at zero books are 2 for Class A and 1 for Class B.

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Using the table, how many Class A students finished exactly one book?
1 mark
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Using the table, how many students are recorded in Class B?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
How many students across both classes finished exactly two books?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Compare the numbers who finished zero or one book.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
A different school compares 8 students out of 10 with 12 students out of 30. Why is comparing 8 and 12 alone unfair?
2 marks
Write a true comparison about the two classes using a number from the table.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Using the table, how many Class A students finished exactly one book?
1 mark
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Read Class A at the value 1 book.
4 students.
Using the table, how many students are recorded in Class B?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Add the frequencies: $1 + 2 + 4 + 3 = 10$ .
10 students.
How many students across both classes finished exactly two books?
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Class A has 3 and Class B has 4.
$3 + 4 = 7$ .
7 students.
Compare the numbers who finished zero or one book.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
Class A: $2 + 4 = 6$ .
Class B: $1 + 2 = 3$ .
Class A: 6; Class B: 3.
A different school compares 8 students out of 10 with 12 students out of 30. Why is comparing 8 and 12 alone unfair?
2 marks
Twelve is a larger count, but it comes from three times as many students.
Compare parts of equally sized groups or proportions before deciding.
The groups have different sizes.
Write a true comparison about the two classes using a number from the table.
2 marks
Practice data: books finished during one week by ten students in each class
Books finished Class A frequency Class B frequency
0 2 1
1 4 2
2 3 4
3 1 3
State the group names and the feature.
Use matching frequencies or combined categories. Other supported comparisons are valid.
For example, 7 of 10 Class B students finished at least two books, compared with 4 of 10 in Class A.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Mathematics Curriculum 2026

Variable types; comparative displays; mode/range/shape; media claims; investigations.

Official curriculum source ↗

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