Relative frequency | Year 7

01 / LEARN

Understand the idea.

Turn a count into a comparison

Frequency counts occurrences; relative frequency describes their share of all valid trials. Seven red results in twenty trials give $\frac{7}{20} = 0.35 = 35 %$ . Dividing by the trial count lets you compare records of different sizes.

Include every valid trial in the denominator, even when the event did not occur. For red, blue results still count as trials. Report both the relative frequency and the trial total so the amount of evidence remains clear.

relative frequency = \frac{observed event count}{all valid trials}

An estimate can change

Relative frequency estimates chance from observations; theoretical probability comes from a model. They may differ because finite experiments vary. Continuing a consistent random procedure tends to make the estimate more stable, although each extra trial need not bring it closer to the model.

To combine comparable records, add the event counts and add the trial totals before dividing. This gives every trial equal weight. Averaging percentages directly gives unequal-sized runs the same influence, even when one contains many more observations.

Example results from 50 spinner trials
Colour	Frequency
Red	22
Blue	15
Green	13

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Estimate a spinner chance

Use the supplied 50-trial table. Estimate the probability of blue.

Example results from 50 spinner trials
Colour	Frequency
Red	22
Blue	15
Green	13

Worked solution

1
Check the trial total from all colour rows.
$22 + 15 + 13 = 50$
Red, blue and green together account for all recorded spinner trials.
2
Divide the blue count by the full total.
$Blue relative frequency = \frac{15}{50} = \frac{3}{10}$
Blue occurred fifteen times among fifty valid trials.
3
Express the estimate as a decimal and percentage.
$\frac{3}{10} = 0.3 = 30 %$
These equivalent forms describe the observed blue share, which estimates rather than fixes its probability.

Answer

Estimated chance $0.3 = 30 %$ .

EXAMPLE 02

Pool unequal-sized records

Two students use the same bag procedure. One gets 9 red in 30 draws and another gets 28 red in 70 draws. Find the combined relative frequency.

Worked solution

1
Pool the red counts.
$9 + 28 = 37$
Both students used the same bag procedure, so their red occurrences can be combined.
2
Pool all the trial counts.
$30 + 70 = 100$
Every valid draw contributes to the denominator, whether red or another colour.
3
Divide the combined counts.
$\frac{37}{100} = 0.37 = 37 %$
Pooling counts weights the seventy-draw record more heavily than the thirty-draw record, in proportion to its number of trials.

Answer

$0.37 = 37 %$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

Heads occurred 18 times in 30 tosses. Find its relative frequency.

Show answer & reasoning

$18 / 30 = 3 / 5 = 0.6$ .

Heads occurred on eighteen of all thirty tosses, so its relative frequency is $\frac{18}{30} = \frac{3}{5} = 0.6$ . The twelve tails are included in the thirty-trial denominator.

Keep practising

6 worksheet questions · 15 marks

Open worksheet Worked solutions

Read the questions online

An event occurred 8 times in 40 trials. Find its relative frequency as a simplified fraction and decimal.
2 marks
Use the supplied spinner record. Find the relative frequency of green.
2 marks
Example results from 50 spinner trials
Colour Frequency
Red 22
Blue 15
Green 13
Use the supplied record. Find the relative frequency of not blue.
2 marks
Example results from 50 spinner trials
Colour Frequency
Red 22
Blue 15
Green 13
A fair-coin model has heads probability 0.5. A 50-toss run has 28 heads. Find its relative frequency and its difference from 0.5.
3 marks
Comparable runs record 6 successes in 10 trials and 36 in 90 trials. Find the pooled relative frequency.
3 marks
Must relative frequency move closer to the theoretical chance whenever one more trial is added? Explain.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

An event occurred 8 times in 40 trials. Find its relative frequency as a simplified fraction and decimal.
2 marks
$\frac{8}{40} = \frac{1}{5}$ .
One fifth is 0.2.
$\frac{1}{5} = 0.2$ .
Use the supplied spinner record. Find the relative frequency of green.
2 marks
Example results from 50 spinner trials
Colour Frequency
Red 22
Blue 15
Green 13
Green occurred 13 times out of 50 trials.
$\frac{13}{50} = 0.26 = 26 %$ .
Use the supplied record. Find the relative frequency of not blue.
2 marks
Example results from 50 spinner trials
Colour Frequency
Red 22
Blue 15
Green 13
Not blue means red or green: $22 + 13 = 35$ .
Divide by 50.
$\frac{35}{50} = 0.7$ .
A fair-coin model has heads probability 0.5. A 50-toss run has 28 heads. Find its relative frequency and its difference from 0.5.
3 marks
$\frac{28}{50} = 0.56$ .
$0.56 - 0.5 = 0.06$ .
0.56, which is 0.06 higher.
Comparable runs record 6 successes in 10 trials and 36 in 90 trials. Find the pooled relative frequency.
3 marks
Total successes: $6 + 36 = 42$ .
Total trials: $10 + 90 = 100$ .
Divide pooled counts, rather than averaging the two percentages equally.
$\frac{42}{100} = 0.42$ .
Must relative frequency move closer to the theoretical chance whenever one more trial is added? Explain.
3 marks
A random next result may move the running proportion nearer or farther away.
Long-run stability does not mean improvement at every step.
No.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 7 single-stage sample spaces, equally likely outcomes, probabilities, expected frequencies, chance experiments, simulations and relative frequencies.

Official curriculum source ↗

In this lesson

Understand the idea.

Turn a count into a comparison

An estimate can change

See the method in action.

Estimate a spinner chance

Check the trial total from all colour rows.

Divide the blue count by the full total.

Express the estimate as a decimal and percentage.

Pool unequal-sized records

Pool the red counts.

Pool all the trial counts.

Divide the combined counts.

Try it yourself.

Check your understanding

Keep practising