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 \frac{20}{100}, 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.

ColourRedYellowWhiteBlue
Relative Frequency    

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 = \frac{25}{94} = 0.27
  • Yellow = \frac{31}{94} = 0.33
  • White = \frac{18}{94} = 0.19
  • Blue = \frac{20}{94} = 0.21

Note: All these relative frequencies should add up to 1.

ColourRedYellowWhiteBlue
Relative Frequency0.270.330.190.21

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 = 0.27 \times 200 = 54
  • Yellow = 0.33 \times 200 = 66
  • White = 0.19 \times 200 = 38
  • Blue = 0.21 \times 200 = 42

The numbers of each colour of jellybeans add up to 200, confirming the accuracy of the estimates.

54 + 66 + 38 + 42 = 200