The idea, step by step
Most frequent, not largest
The mode is the value or category that occurs most often. Sort a short list or count each value in a frequency table. The largest number is not necessarily the mode: frequency tells how often a value appears.
For 2, 3, 3, 3, 6, the value 3 appears three times. The mode is 3, although 6 is the largest value.
Tied modes and no mode
Two or more values can tie for the highest frequency. State each tied mode when that highest frequency is greater than one. In this lesson, if every value appears once, we describe the list as having no mode.
A mode can help summarise category choices, such as the most popular fruit. It does not describe every person: pupils who chose another fruit remain part of the data.
| Fruit | Votes |
|---|---|
| Apples | 8 |
| Bananas | 6 |
| Oranges | 4 |
| Pears | 2 |
A common trap
The mode is always the biggest number.
Instead: Find the value with the greatest frequency, not the greatest size.
See the thinking
Count each value
Find the mode of 4, 6, 4, 7, 6, 4, 8.
- 4 occurs three times.
- 6 occurs twice; 7 and 8 occur once.
- The greatest frequency belongs to 4.
A tie
Find the modes of 2, 5, 2, 7, 5, 9.
- 2 occurs twice and 5 occurs twice.
- 7 and 9 occur once.
- Both 2 and 5 have the greatest frequency.
Check your understanding
Find the mode of 3, 8, 3, 4, 3, 8.
Show answer
3.
3 occurs three times, 8 twice and 4 once.
Your turn
6 questions · 8 marks · Work at your own pace.
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.
6 + 4 = 10 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 ↗