Understand the idea.
Mode and range answer different questions
To find the mode, count how often each value appears. Choose the value with the greatest frequency, rather than the largest value. If repeated values tie for the highest frequency, list each of them; in this course, no repeats means no mode.
To find the range, subtract the smallest recorded value from the largest. It measures the full span of the data and uses the data's units. The number of entries tells you the size of the data set, not its range.
Look at the whole shape
Order the values or use a suitable display to examine the whole distribution. Look for a cluster where several values lie close together, gaps with no values, and any observation far from the rest. Name the actual values in your description.
The sets and both have range , yet their clusters are in different places. A mode and a range each describe one feature; neither replaces looking at all the data.
See the method in action.
A mode and a range
Find the mode and range of 3, 5, 5, 6, 9.
Worked solution
- 1
Count each value's frequency.
The value five occurs more often than any other value, so the mode is five.
- 2
Identify the two extremes.
Only the smallest and largest values are needed to calculate the range.
- 3
Subtract smallest from largest.
The distance from three to nine is six, giving mode five and range six.
Mode 5; range 6.
An unusual value
Describe 4, 4, 5, 5, 6, 18 using mode, range and shape.
Worked solution
- 1
Find the greatest frequency.
Four and five tie for the greatest frequency, so both are modes.
- 2
Calculate the range.
Eighteen is the largest value and four is the smallest.
- 3
Locate the main cluster.
Five of the six values lie between four and six.
- 4
Describe the separated value.
Eighteen lies twelve above the next largest value, making it unusually high compared with the cluster.
Modes 4 and 5; range 14; a cluster from 4 to 6 and an unusually high value at 18.
Try it yourself.
Check your understanding
Find the range of 7, 7, 9, 12.
Show answer & reasoning
5.
The smallest value is and the largest is . The repeated seven does not change these extremes, so the range is .
Keep practising
6 worksheet questions · 11 marks
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 ↗