The idea, step by step
Mode and range answer different questions
The mode is the value occurring most often. For this course, if no value repeats, say there is no mode. If two or more repeated values tie for the greatest frequency, list all of them as modes. Count frequencies rather than choosing the largest number.
The range measures the distance from the smallest recorded value to the largest: largest minus smallest. A range alone does not tell us where most values lie.
Look at the whole shape
Arrange numerical data in order or draw a suitable display. Describe where values cluster, whether there are gaps and whether any value is unusually far from the others. Use the data to support your words.
The sets 2, 3, 3, 4, 8 and 2, 5, 5, 6, 8 both have range 6. The second set is more concentrated around 5 and 6. Equal ranges do not make two distributions identical.
A common trap
Range is the number of entries in the list.
Instead: Count entries to find the data-set size. Subtract smallest from largest to find range.
See the thinking
A mode and a range
Find the mode and range of 3, 5, 5, 6, 9.
- The value 5 occurs twice; each other value occurs once.
- The largest value is 9 and the smallest is 3.
- .
An unusual value
Describe 4, 4, 5, 5, 6, 18 using mode, range and shape.
- The modes are 4 and 5, each occurring twice.
- Range: .
- Five values cluster from 4 to 6; 18 is separated by a large gap.
Check your understanding
Find the range of 7, 7, 9, 12.
Show answer
5.
The extreme values are 12 and 7, so .
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Find the mode of 2, 3, 3, 4, 6.1 mark
- Find the range of 11, 8, 15, 10.2 marks
- Find all modes of 1, 1, 2, 3, 3, 4.2 marks
- What is the range of 6, 6, 6, 6?2 marks
- Describe a cluster and an unusual value in 9, 10, 10, 11, 12, 30.2 marks
- Set A is 1, 2, 2, 3, 7. Set B is 1, 5, 5, 6, 7. Both have range 6. Give one difference.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the mode of 2, 3, 3, 4, 6.1 mark
3 occurs twice; all other values occur once.
3. - Find the range of 11, 8, 15, 10.2 marks
Largest 15, smallest 8.
.
7. - Find all modes of 1, 1, 2, 3, 3, 4.2 marks
Each occurs twice, the joint greatest frequency.
1 and 3. - What is the range of 6, 6, 6, 6?2 marks
Largest and smallest are both 6.
.
0. - Describe a cluster and an unusual value in 9, 10, 10, 11, 12, 30.2 marks
Five observations lie close together from 9 to 12.
There is a gap of 18 between 12 and 30.
A cluster from 9 to 12 and an unusually high value at 30. - Set A is 1, 2, 2, 3, 7. Set B is 1, 5, 5, 6, 7. Both have range 6. Give one difference.2 marks
Check the most common values.
Do not assume matching ranges mean matching distributions.
For example, A has mode 2 while B has mode 5; most B values are higher.
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 ↗