Relative frequency | Year 7

01 / LEARN

The idea, step by step

Turn a count into a comparison

Frequency is a count; relative frequency is event count divided by all trials. This allows different-sized experiments to be compared. Seven red results in 20 trials give $7 / 20 = 0.35 = 35 %$ .

Use all valid trials as the denominator. A blue result still counts as a trial when you calculate red relative frequency. State the trial count alongside the proportion so the reader knows the size of the record.

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

An estimate can change

Relative frequency estimates chance from a finite record. It can differ from a theoretical probability and change when trials are added. More trials often give a more stable estimate, but it need not move closer after every trial.

For comparable experiments, pool results by adding event counts and all trial counts first. Do not simply average percentages from unequal-sized runs: a 10-trial and a 100-trial run should not receive equal weight.

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

A common trap

The observed fraction is the exact chance the next result must follow.

Instead: It is an estimate from a record. The next result remains uncertain, and the estimate may change.

02 / WORKED EXAMPLES

See the thinking

Example 1

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

Blue occurred 15 times.
The total is $22 + 15 + 13 = 50$ .
$15 / 50 = 3 / 10 = 0.3$ .

Estimated chance

0.3 = 30 %

Example 2

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.

Total red: $9 + 28 = 37$ .
Total trials: $30 + 70 = 100$ .
Divide the combined counts: $37 / 100 = 0.37$ .

0.37 = 37 %

Check your understanding

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

Show answer

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

Divide by all 30 tosses, not by the 12 tails.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF 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
$8 / 40 = 1 / 5$ .
One fifth is 0.2.
$1 / 5 = 0.2$ .
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.
$13 / 50 = 0.26 = 26 %$ .
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.
$35 / 50 = 0.7$ .
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
$28 / 50 = 0.56$ .
$0.56 - 0.5 = 0.06$ .
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.
$42 / 100 = 0.42$ .
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.

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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 ↗

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