The idea, step by step
Count what happened
An observed frequency is the number of times an outcome actually appeared. It is a count from completed trials. In the example table, red appeared 14 times in 30 spins. This records what happened, not a promise about the next spin.
Add all outcome frequencies to check the number of recorded trials. Compare counts only after checking that the groups used the same number of trials.
| Colour | Frequency |
|---|---|
| Red | 14 |
| Blue | 9 |
| Green | 7 |
Comparing different trial counts
If one group performs 10 trials and another performs 50, the larger group has more opportunities to record every outcome. A larger raw count does not by itself show an outcome occurred more often in proportion.
For example, 6 successes in 10 trials and 30 successes in 50 trials have the same share: making five copies of 6 out of 10 gives 30 out of 50. We can describe the observed share without claiming it is the exact chance.
| Group | Successes | Trials |
|---|---|---|
| A | 6 | 10 |
| B | 30 | 50 |
A common trap
The most frequent result in one experiment must be most likely or must happen next.
Instead: A frequency records past trials. Chance variation and the design of the device must be considered before wider claims.
See the thinking
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 |
- Red has the greatest frequency, 14.
- Green has frequency 7.
- 14 − 7 = 7.
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?
- Scale Group A's counts by five: 4 × 5 = 20 and 10 × 5 = 50.
- Both records therefore describe the same share.
- The larger raw count comes with a larger number of trials.
Check your understanding
A record shows 9 red, 7 blue and 4 yellow results. How many trials were recorded?
Show answer
20.
9 + 7 + 4 = 20; each trial contributes one outcome.
Your turn
6 questions · 9 marks · Work at your own pace.
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 14 + 9 + 7 = 30.
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
8 + 12 = 20.
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 12 − 8 = 4.
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 ↗