Understand the idea.
A list keeps the original answers
A response list keeps each answer in the order it was recorded. In apple, pear, apple, banana, pear, apple, a repeated word means another response. Three apple entries mean three apple choices, not just one fruit name.
Choose one fruit and scan the whole list for it. Mark each matching entry as you count, then repeat for the other fruits. This gives apple , pear and banana , with each response counted once.
A table organises the count
A frequency table gathers the repeated answers into groups. Put each fruit name in its own row and write its count beside it. The headings tell readers that the numbers are responses, rather than pieces of fruit.
Add the counts: . There are six entries in the list, so the total agrees. Still check each fruit's count: a matching total alone cannot show that every response is in the right group.
| Fruit | Responses |
|---|---|
| Apple | 3 |
| Pear | 2 |
| Banana | 1 |
See the method in action.
Organise a colour list
Make a table for: blue, red, blue, green, red, blue.
| Colour | Responses |
|---|---|
| Blue | 3 |
| Red | 2 |
| Green | 1 |
Worked solution
- 1
Give each different colour one row.
Blue, red and green are the three choices; repeated words belong in the same colour's row.
- 2
Count the entries for each colour.
Blue appears in positions one, three and six; red in positions two and five; green in position four.
- 3
Check that all six responses are included.
The table's counts total six, matching the six entries in the original list.
Blue: 3; red: 2; green: 1.
Find a recording error
A child counts the fruit choices as Apple 3, Pear 2, Banana 2. Does that match the original table?
| Child | Choice |
|---|---|
| Ari | Apple |
| Bo | Pear |
| Cleo | Apple |
| Dara | Banana |
| Eli | Pear |
| Finn | Apple |
Worked solution
- 1
Add the child's recorded counts.
These counts would mean seven responses, but the original table lists only six children.
- 2
Check who chose each fruit in the original table.
Ari, Cleo and Finn chose apple; Bo and Eli chose pear; only Dara chose banana.
- 3
Replace the banana count and check again.
Banana must be one. The corrected counts now agree with every child's choice and the six-child total.
No. Banana should be 1, making 6 responses in all.
Try it yourself.
Check your understanding
A list says cat, dog, cat, fish, dog, cat. How many cat responses are there?
Show answer & reasoning
3.
Scan the whole list and mark each cat entry. Cat is first, third and sixth, so there are three cat responses. The dog and fish entries belong to other groups.
Keep practising
6 worksheet questions
Read the questions online
- Count the apple choices in the fruit table.
Six children choose one fruit each. Child Choice Ari Apple Bo Pear Cleo Apple Dara Banana Eli Pear Finn Apple - Make a frequency table for: bus, walk, walk, car, walk, bus.
- How many vehicles are recorded altogether?
Vehicles observed in five minutes. Vehicle Number Car 6 Bus 2 Bicycle 3 - Write the book types from the fewest choices to the most.
Books chosen by a group. Type Number Animals 4 Space 2 Stories 5 - Seven children each give one answer to a survey. A table shows responses. Explain why it needs checking.
- Use the weather record to make a frequency table for Sunny, Cloudy and Rainy.
Weather observed over five school days. Day Weather Monday Sunny Tuesday Cloudy Wednesday Sunny Thursday Rainy Friday Sunny
Read the worked solutions
- Count the apple choices in the fruit table.
Six children choose one fruit each. Child Choice Ari Apple Bo Pear Cleo Apple Dara Banana Eli Pear Finn Apple Ari, Cleo and Finn chose apple.
3. - Make a frequency table for: bus, walk, walk, car, walk, bus.
Count each choice once.
Check .
Bus: 2; walk: 3; car: 1. - How many vehicles are recorded altogether?
Vehicles observed in five minutes. Vehicle Number Car 6 Bus 2 Bicycle 3 .
11 vehicles. - Write the book types from the fewest choices to the most.
Books chosen by a group. Type Number Animals 4 Space 2 Stories 5 Their counts are .
Space, Animals, Stories. - Seven children each give one answer to a survey. A table shows responses. Explain why it needs checking.
.
Check for a repeated response in the original records.
The counts total 8, but only 7 children answered. - Use the weather record to make a frequency table for Sunny, Cloudy and Rainy.
Weather observed over five school days. Day Weather Monday Sunny Tuesday Cloudy Wednesday Sunny Thursday Rainy Friday Sunny Monday, Wednesday and Friday are sunny.
Tuesday is cloudy and Thursday is rainy.
The total is 5 days.
Sunny: 3; Cloudy: 1; Rainy: 1.
Curriculum reference & lesson scope
Australian Curriculum v9; SA Curriculum Mathematics 2026
Surveys/observations; lists/tables; creating displays; comparing representations and conclusions.
Official curriculum source ↗