Relative frequency and expected outcomes

Relative frequency

• Relative frequency = number of times an event happens ÷ number of trials. It is an estimate of the probability, found by experiment.
• A drawing pin lands point up 36 times in 120 throws. The relative frequency is 36/120 = 0.3.
• The more trials you do, the more reliable the estimate.

Expected outcomes

• Expected number = probability × number of trials.
• A fair dice rolled 300 times should give about 300 × 1/6 = 50 sixes.
• If P(late) = 0.15, you would expect about 0.15 × 200 = 30 late trains in 200 journeys.

Fair or biased?

• A fair (unbiased) object has equally likely outcomes. If the results over many trials are very different from what you'd expect, the object may be biased.
• A coin that lands on heads 70 times in 100 flips may well be biased. 7 heads in 10 flips is not enough evidence.

Frequency trees and two-way tables

• A frequency tree shows how a group splits into categories, then into more categories.
• A two-way table shows data sorted by two sets of categories. Use the totals to find probabilities.

Key terms

Relative frequency

The number of times an event happens ÷ the number of trials.

Trial

One go at an experiment, such as one roll of a dice.

Expected outcome

Probability × number of trials.

Biased

Not fair: the outcomes are not equally likely.

Frequency tree

A diagram showing how a group splits into categories.

Two-way table

A table showing data sorted by two sets of categories.