L1 · Frequency and relative frequency

Learning goal

“I can find the frequency of an outcome from an experiment's results, and its relative frequency - the frequency divided by the total number of trials - written as a fraction in simplest form. I know the relative frequencies of all the outcomes add to 1.”

Outcome — one possible result of an experiment, like "the spinner lands on red".

Frequency — how many times an outcome actually happened. If red landed 8 times, its frequency is 8.

Total trials — how many times the experiment was done altogether. Every spin, toss, or draw counts as one trial.

Relative frequency — the frequency compared with the total: relative frequency = frequency / total trials. It is a fraction of 1, like 8/20 = 2/5.

Worked example

A spinner was spun 20 times. Results: red landed 8 times, blue 7 times, green 5 times. Step 1: The frequencies are the counts: red 8, blue 7, green 5. Check the total trials: 8 + 7 + 5 = 20 - matches the 20 spins. Step 2: The relative frequency compares the count with the total. For red: 8 / 20, written as the fraction 8/20. Step 3: Simplify: 8/20 = 2/5. Say it plainly: frequency is a count; relative frequency is the count's share of the total.

Check yourself — explain it

The relative frequency of red is 2/5, not 8, because...

Paired problem — example still visible

A coin was tossed 30 times: heads 17, tails 13. What is the relative frequency of tails? -> 13/30 (13 / 30; 13/30 is already in simplest form)

Faded completion — last step is yours

"A die was rolled 24 times and 6 came up 9 times. Relative frequency of 6: 9/24 = ___/8." -> 3 (9/24 = 3/8)

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