### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Relative Frequency

The relative frequency of an event is a measure of how many times that event occurs in a certain number of trials.

For example, out of 100 schoolchildren, 20 might wear glasses. Therefore, the relative frequency of wearing glasses in the school would be , or 0.2.

## Example: Calculating Relative Frequency

Josie decides to investigate the number of each colour of jellybeans in a box. Here are her results:

• Red: 25
• Yellow: 31
• White: 18
• Blue: 20

Write down the relative frequency of each colour in the table below.

Solution:

To find the relative frequency of each colour, divide the number of beans of that colour by the total number of beans tested (94).

• Red • Yellow = • White • Blue Note: All these relative frequencies should add up to 1.

Now we can use these relative frequencies to estimate how many of each colour would be in a larger packet.

### Using relative frequency to estimate

Josie buys a larger packet of 200 jellybeans. Estimate the number of each colour jellybean in the packet.

Solution:

For each colour, we have the relative frequency as calculated previously. This tells us the proportion of each colour as a decimal.

To find the estimated number of each colour, simply multiply the relative frequency by the 200 total jellybeans:

• Red • Yellow • White • Blue The numbers of each colour of jellybeans add up to 200, confirming the accuracy of the estimates. 