Succeed with maths – Part 2

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# 1.4 Finding the mode of a data set

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

In some data sets, more than one value occurs most frequently, so there is then actually more than one mode. The mode is fairly easy to find, but it does not consider all the values in a 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 of a data set can be summarised as follows:

• Arrange all the values in numerical order.
• Choose the value (or values) that occur most frequently.

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

## Table 5 Charlie's first set of scores

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

Arranging Charlie’s scores in numerical order gives:

250, 270, 270, 290, 290, 300

Two of the scores occur twice in this set, so there are two modal values: 270 and 290.

Try finding the mode yourself in this next activity.

## Activity 4 Finding the mode of a data set

Timing: Allow approximately 4 minutes

Charlie’s set of scores for her next week of play is shown below:

### Table 6 Charlie’s scores for her next week of play

 Monday Tuesday Wednesday Thursday Friday Saturday Sunday 270 260 280 270 310 300 290

Find the mode for this week’s scores.

Arranging Charlie’s scores in order gives: 260, 270, 270, 280, 290, 300, 310.

Each score occurs once, except 270 which occurs twice. The mode is therefore again 270.

This is perhaps not as representative this time of Charlie’s typical score though, as 270 is at the lower end of the range. The median value of 280, or mean of 283 are probably better this time.

It’s not really that important if you had one or other of these values for Charlie’s typical score but didn’t know which average had been used. However, in other situations this may not be the case. A specific average may be picked to support a particular point of view in the media or when arguing a case. You’ll have a look at this in the next brief section.