Understand the idea.
Most frequent, not largest
To find the mode, count how often each different value appears. These counts are frequencies. The value with the greatest frequency is the mode: ask which value appears most often, rather than which value is largest.
Sorting can make repeats easier to see. In , the value appears three times, while and appear once each. The mode is ; its frequency is three.
Tied modes and no mode
Check for a tie before naming one mode. If several values share the greatest frequency and that frequency is greater than one, report them all. In this lesson, a list in which every value appears once has no mode.
Categories can have a mode too. Apples have the most votes in the fruit table, so apples are the modal choice. This describes the most popular single choice; it does not mean that everyone chose apples.
| Fruit | Votes |
|---|---|
| Apples | 8 |
| Bananas | 6 |
| Oranges | 4 |
| Pears | 2 |
See the method in action.
Count each value
Find the mode of 4, 6, 4, 7, 6, 4, 8.
Worked solution
- 1
Group the repeated values.
Sorting the list groups equal values without adding or removing any entries.
- 2
Count the frequency of each value.
Frequency counts appearances; the seven appearances account for the whole original list.
- 3
Name the value with greatest frequency.
The value appears three times, more often than any other value.
The mode is 4.
A tie
Find the modes of 2, 5, 2, 7, 5, 9.
Worked solution
- 1
Group the values in order.
Putting equal values together makes both repeated groups visible.
- 2
Compare all four frequencies.
Both and share the greatest frequency; neither of the other values matches it.
- 3
Report both tied modes.
Every value tied for the highest repeated frequency must be included.
The modes are 2 and 5.
Try it yourself.
Check your understanding
Find the mode of 3, 8, 3, 4, 3, 8.
Show answer & reasoning
3.
In , the frequencies are three appearances of , two of and one of . Therefore is the mode, even though is the largest value.
Keep practising
6 worksheet questions · 8 marks
Read the questions online
- Find the mode of 1, 2, 2, 2, 5.1 mark
- Find the modes of 6, 4, 6, 4, 9.1 mark
- Find the mode of 2, 4, 7, 9, using this lesson's convention.1 mark
- Which fruit is the mode in the supplied table?1 mark
One vote from each of 20 fictional students Fruit Votes Apples 8 Bananas 6 Oranges 4 Pears 2 - A list is 5, 5, 5, 8, 9. Another 9 is added. Does its mode change?2 marks
- A shop sells 6 small, 10 medium and 4 large hats. Which size is the mode? Did everyone choose it?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the mode of 1, 2, 2, 2, 5.1 mark
2 occurs three times; the other values occur once.
2. - Find the modes of 6, 4, 6, 4, 9.1 mark
Both 4 and 6 occur twice; 9 occurs once.
4 and 6. - Find the mode of 2, 4, 7, 9, using this lesson's convention.1 mark
Each value occurs once; none is more frequent.
No mode. - Which fruit is the mode in the supplied table?1 mark
One vote from each of 20 fictional students Fruit Votes Apples 8 Bananas 6 Oranges 4 Pears 2 Apples have the largest frequency: 8 votes.
Apples. - A list is 5, 5, 5, 8, 9. Another 9 is added. Does its mode change?2 marks
5 still occurs three times.
9 now occurs twice, so it is not most frequent.
No; the mode remains 5. - A shop sells 6 small, 10 medium and 4 large hats. Which size is the mode? Did everyone choose it?2 marks
Medium has the most sales.
sales were not medium.
Medium. No: 10 hats sold were other sizes.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum 2026
Data types/validation; mode; suitable displays; line graphs; statistical investigations.
Official curriculum source ↗