Understand the idea.
Count what happened
An observed frequency counts what actually happened in completed trials. Red has frequency in the spin table, meaning fourteen of those spins gave red. This is a record of the experiment, not a guarantee about the next spin.
Add the frequencies to check the trial total: . Within this record, a greater frequency means more occurrences. When comparing separate groups, check their trial totals too, because a longer experiment gives more opportunities to record an outcome.
| Colour | Frequency |
|---|---|
| Red | 14 |
| Blue | 9 |
| Green | 7 |
Comparing different trial counts
Compare observed shares when the trial totals differ. Scale the successes and the trial count by the same factor so the totals match. Multiplying both preserves the share; multiplying only successes would change the result you are comparing.
For example, successes in trials can be compared with in : five copies of the first record have successes in trials. Equal observed shares do not prove that either share is the device's exact chance.
| Group | Successes | Trials |
|---|---|---|
| A | 6 | 10 |
| B | 30 | 50 |
See the method in action.
Read a record
In the 30-spin table, which colour occurred most often, and how many more times did it occur than green?
| Colour | Frequency |
|---|---|
| Red | 14 |
| Blue | 9 |
| Green | 7 |
Worked solution
- 1
Compare the three observed frequencies.
Red's fourteen occurrences exceed blue's nine and green's seven, so red occurred most often.
- 2
Read the green count needed for the comparison.
The question asks how many more times red occurred than green, so use green rather than the next-largest count.
- 3
Subtract green's count from red's count.
The difference shows that red occurred seven more times than green in this thirty-spin record.
Red occurred most often, 7 more times than green.
A fair comparison
Group A records 4 heads in 10 tosses. Group B records 20 heads in 50 tosses. Did one have a larger share of heads?
Worked solution
- 1
Scale Group A's trial total to match Group B.
Comparing both records over fifty trials gives their head counts the same-sized total.
- 2
Scale Group A's head count by the same factor.
Scaling both counts together keeps Group A's observed share unchanged.
- 3
Compare the shares using the matched totals.
Both records have twenty heads per fifty tosses when put on the same scale, so neither has a larger observed share.
No. Both observed the same share of heads.
Try it yourself.
Check your understanding
A record shows 9 red, 7 blue and 4 yellow results. How many trials were recorded?
Show answer & reasoning
20.
Each trial contributes one result to exactly one colour count. Adding all three counts gives , so the record contains twenty trials.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- How many trials are recorded in the supplied spin table?1 mark
Example results from 30 spins Colour Frequency Red 14 Blue 9 Green 7 - Which colour occurred least often in that table?1 mark
Example results from 30 spins Colour Frequency Red 14 Blue 9 Green 7 - A record shows Win 8 and Lose 12. How many trials are recorded, and which outcome is more frequent?2 marks
- A coin record shows 12 heads and 8 tails. How many more heads than tails occurred?1 mark
Example results from 20 tosses of a fair coin Outcome Frequency Heads 12 Tails 8 - Group A records red 3 times in 10 trials. Group B records red 15 times in 50 trials. Compare their observed shares.2 marks
- A hidden spinner gives blue 9 times in 10 spins. Can you be certain it has nine blue sectors out of ten? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- How many trials are recorded in the supplied spin table?1 mark
Example results from 30 spins Colour Frequency Red 14 Blue 9 Green 7 .
30. - Which colour occurred least often in that table?1 mark
Example results from 30 spins Colour Frequency Red 14 Blue 9 Green 7 Its frequency, 7, is smaller than 9 and 14.
Green. - A record shows Win 8 and Lose 12. How many trials are recorded, and which outcome is more frequent?2 marks
.
12 is greater than 8.
20 trials; Lose is more frequent. - A coin record shows 12 heads and 8 tails. How many more heads than tails occurred?1 mark
Example results from 20 tosses of a fair coin Outcome Frequency Heads 12 Tails 8 .
4. - Group A records red 3 times in 10 trials. Group B records red 15 times in 50 trials. Compare their observed shares.2 marks
Multiplying 3 and 10 by five gives 15 and 50.
The shares are equal. - A hidden spinner gives blue 9 times in 10 spins. Can you be certain it has nine blue sectors out of ten? Explain.2 marks
Different spinner designs could produce that record.
Inspect the device or collect more evidence before making a stronger claim.
No. A short trial record does not show the exact sector arrangement.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum 2026
Listing outcomes; equal/unequal likelihood; repeated trials; observed frequencies.
Official curriculum source ↗