Understand the idea.
Describe the whole set
A distribution describes how responses are spread across values. In the pet table, the first column tells the number of pets; the second tells how many children gave that answer. Keep those two meanings separate.
Five children have 1 pet, more than any other group. Three children have no pets, three have 2 pets, and one has 3 pets. The recorded pet counts extend from 0 to 3.
| Number of pets | Number of children |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 3 |
| 3 | 1 |
Compare using evidence
Describe a pattern using the counts: where do responses gather, and which values are uncommon? Support the description with numbers. A large pet count for one child does not mean that most children have many pets.
When comparing groups, first check their numbers of responses. For groups of the same size, compare how often each value occurs. Two groups can have the same lowest and highest values but different patterns between them.
See the method in action.
Most common count
What number of pets is most common in the supplied table?
| Number of pets | Number of children |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 3 |
| 3 | 1 |
Worked solution
- 1
Read the frequencies, not just the pet counts.
Frequency tells how many children gave each response.
- 2
Find the greatest frequency.
The greatest frequency identifies the most common response.
- 3
Read the pet count beside that frequency.
The row with five children corresponds to one pet, not five pets.
1 pet.
Different patterns
Class A records 0, 1, 1, 1, 2 pets. Class B records 0, 0, 1, 2, 2. Describe one difference.
Worked solution
- 1
Check that the groups contain the same number of responses.
Equal group sizes allow a direct comparison of their frequencies.
- 2
Count the one-pet responses.
Class A has more responses at the middle value of one pet.
- 3
Count responses at zero or two pets.
Class B has more responses at the two ends, while A is more concentrated at one pet.
- 4
Describe the difference.
A gathers more at one pet; B is more spread among zero and two, although both lists run from zero to two.
A is more concentrated at 1 pet; B is more spread among 0 and 2.
Try it yourself.
Check your understanding
For 1, 1, 2, 2, 2, 3, which value appears most often?
Show answer & reasoning
2.
The value 1 occurs twice, 2 occurs three times, and 3 occurs once. The largest frequency is three, so 2 is the most common value.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- Using the supplied pet table, which number of pets is least common?1 mark
Practice data: pets owned by 12 children Number of pets Number of children 0 3 1 5 2 3 3 1 - How many children are represented in the pet table?1 mark
Practice data: pets owned by 12 children Number of pets Number of children 0 3 1 5 2 3 3 1 - Which value is most common in 2, 3, 3, 3, 4, 5?1 mark
- Describe the values recorded in 4, 4, 5, 5, 5, 6.2 marks
- Compare 2, 2, 3, 3, 4 with 0, 2, 3, 4, 6. Which list is more spread out? Explain.2 marks
- One child has 10 pets while most have 0, 1 or 2. Can you say that most children have 10 pets? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Using the supplied pet table, which number of pets is least common?1 mark
Practice data: pets owned by 12 children Number of pets Number of children 0 3 1 5 2 3 3 1 Only one child has 3 pets.
3 pets. - How many children are represented in the pet table?1 mark
Practice data: pets owned by 12 children Number of pets Number of children 0 3 1 5 2 3 3 1 .
12 children. - Which value is most common in 2, 3, 3, 3, 4, 5?1 mark
It appears three times.
3. - Describe the values recorded in 4, 4, 5, 5, 5, 6.2 marks
5 appears three times;4 appears twice and 6 once.
They run from 4 to 6 and are concentrated at 5. - Compare 2, 2, 3, 3, 4 with 0, 2, 3, 4, 6. Which list is more spread out? Explain.2 marks
It extends from 0 to 6, while the first extends only from 2 to 4.
The second list. - One child has 10 pets while most have 0, 1 or 2. Can you say that most children have 10 pets? Explain.2 marks
Describe the frequencies of the whole set.
No. 10 is an unusual value, not a common response.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Scaled pictographs/column graphs; data collection; suitable displays; distributions; survey investigations.
Official curriculum source ↗