Relative Frequency

20 min
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When you actually run an experiment — tossing a coin, rolling a die, spinning a spinner — the relative frequency of an outcome is:

relative frequency=number of times the outcome happenedtotal number of trials\text{relative frequency} = \frac{\text{number of times the outcome happened}}{\text{total number of trials}}

It is an experimental estimate of how likely the outcome is, usually written as a fraction, decimal or percentage.

For example, if a coin lands heads 3030 times in 5050 tosses, the relative frequency of heads is 3050=0.6\dfrac{30}{50} = 0.6. The more trials you run, the closer the relative frequency tends to settle towards the true probability.

Worked example. A die is rolled 6060 times and shows a six on 1212 of them. Relative frequency of a six =1260=0.2= \dfrac{12}{60} = 0.2.

Relative frequency of an outcome is calculated as…

A coin is tossed 5050 times and lands heads 3030 times. What is the relative frequency of heads, as a decimal?

A die is rolled 6060 times and shows a six 1212 times. What is the relative frequency of a six, as a decimal?

In 200200 spins of a spinner it lands on green 5050 times. What is the relative frequency of green, as a decimal?