11.1.5 Finding the Mode of a Data Set

Another method of finding an average is simply to pick the value that occurs most often. The value that occurs most often is known as the mode or the modal value.

In some data sets, more than one value occurs most frequently and so there is more than one mode. The mode is fairly easy to find, but it does not consider all the values in the data set. However it can be useful in some situations, such as when making decisions about which sizes of a particular piece of clothing should be stocked in a shop.

Finding the Mode

Finding the mode of a data set can be summarized as follows:

  • Arrange all the values in ascending or descending order.
  • Choose the value (or values) that occurs most frequently.
  • Write down the conclusion and include the units.

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From the previous example, Charlie’s first set of scores is shown below:

Charlie’s Scores

Monday Tuesday Wednesday Thursday Friday Saturday
450 470 430 490 490 220

Arranging Charlie’s scores in order gives: 220, 430, 450, 470, 490, 490.

Each score occurs once, except for the score of 490, which occurs twice.

So, the mode (or the modal score) is 490.

In this case, the mode is the highest score. Do you think this is a good way of describing Charlie’s typical score?

Solution symbolActivity: Finding the Mode of a Data Set

Charlie’s second set of scores is shown below:

Charlie’s Scores

Monday Tuesday Wednesday Thursday Friday Saturday Sunday
250 270 300 290 320 290 270

Find the two modal values.

Solution symbol

Answer

Arranging Charlie’s scores in order gives: 250, 270, 270, 290, 290, 300, 320.

Each score occurs once, except 270 and 290, which both occur twice. The modal scores are therefore 270 and 290.

11.1.4 More Means and Medians

11.1.6 Using Different Averages