The idea, step by step
Describe the whole set
A distribution shows how the data are spread among possible values. In this practice pet table, 1 pet is the most common response because it has the largest frequency. There are some zero-pet and two-pet responses, and only one child has three pets.
| Number of pets | Number of children |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 3 |
| 3 | 1 |
Compare using evidence
Describe where values gather, which are less common and how far the recorded values extend. Use counts to support statements. A single unusual value does not describe everyone. When comparing two groups, check how many responses each group contains before comparing their frequencies.
A common trap
The largest data value must be the most common.
Instead: A value’s size and its frequency are different. Read how often the value occurs.
See the thinking
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 |
- Look at the frequency column.
- The largest frequency is 5.
- It belongs to 1 pet.
Different patterns
Class A records 0, 1, 1, 1, 2 pets. Class B records 0, 0, 1, 2, 2. Describe one difference.
- Both lists contain five children.
- A has three one-pet responses; B has one.
- B has more responses at the ends, 0 and 2.
Check your understanding
For 1, 1, 2, 2, 2, 3, which value appears most often?
Show answer
2.
The value 2 occurs three times.
Your turn
6 questions · 9 marks · Work at your own pace.
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 3 + 5 + 3 + 1 = 12.
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 ↗