Foundation and Higher · relative frequency

Relative frequency.
Probability from
an experiment.

more trials,
better estimate

when you cannot work it out in theory —

Experiment

do it lots of times and count

that is how often ÷ how many

step 1 of 4

Work it out

1. Times it happened over number of trials.

2. 32 ÷ 50 = 0.64.

✓ An estimate of the probability

drawing pin dropped 50 times

lands point up 32 times

3250 = 0.64

step 2 of 4

More trials is better

1. Early on it jumps about.

2. With more trials it settles down.

✓ It is settling near 0.6

step 3 of 4

Is it fair?

1. Fair dice: each number about 100 times.

2. 170 is a long way from 100.

✓ Compare expected with actual

a dice rolled 600 times

expect 600 ÷ 6 = 100 sixes

actual sixes = 170

probably biased

step 4 of 4

Use it to predict

1. Treat it like a probability.

2. Multiply by the number of trials.

✓ Expect about 128

relative frequency = 0.64

next 200 drops

0.64 × 200 = 128 point up

relative frequency —

Formula

times it happened ÷ trials

Reliability

more trials is better

Bias

compare expected with actual

Asked for the best estimate?
Use the one with the most trials.

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