Relative frequency
The working out of probabilities through some given
evidence.
Relative frequency means probability so the answers must be
between 0 and 1.
Relative Frequency
Example
A spinner with five edges numbered 1 to 5 is spun 20 times and the results are shown
below.
1 4 3 3 4 5 1 2 1 3
4 5 1 3 4 2 2 1 5 4
Complete the table of relative frequencies below.
Number
on
spinner
Relative
Frequency
1
2
3
4
5
Example
The Bumbleton and Stickton village football teams have played each other 50
times.
Bumbleton have won 10 times, Stickton have won 35 times, and the teams have
drawn 5 times.
Estimate the probability that Stickton will win the next match
Example
Matthew decides to try to estimate the probability that toast lands butter-sidedown when dropped.
He drops a piece of buttered toast 50 times and observes that it lands butter-sidedown 30 times.
Estimate the probability that the toast lands butter-side-down.
Example
A drawing pin can land 'point up' or 'point down' when dropped.
Jim drops a drawing pin 100 times and it lands "point up" 35 times.
Estimate the probability of the drawing-pin landing "point up"
Example
A spinner has a red sector (R) and a yellow sector (Y).
The arrow is spun 1000 times.
The table shows the relative frequency of a red after
different numbers of spins.
Red
Yellow
Number of spins
Relative frequency
of a red
50
0.42
100
0.36
200
0.34
500
0.3
1000
0.32
a) How many times was a red obtained after 200 spins?
b) Which relative frequency gives the best estimate of the probability of a red? Explain
your answer.
Example
A dice is suspected of bias. Here are the results of 20 throws
3
4
2
3
1
5
6
2
4
3
4
3
1
1
6
2
5
6
5
3
(a) Use these results to calculate the relative frequency of each score
Score
1
2
3
4
5
Relative frequency
(b) Use the relative frequency to calculate how many times you would
expect to score 3 in 60 throws of this dice.
(c) Compare your answer to part (b) with the number of times you
would expect to score 3 in 60 throws of a fair dice.
6