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Lesson 3, Topic 4
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# The Mode

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The mode is the number that appears most often. Also, the mode is the value that occurs most frequently in a set of data. The frequency is the number of times that a data value appears.

A set of data may have more than one mode

### Example:

Find the mode of these numbersÂ

(i) 2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3
(ii) 4, 1, 4, 2, 4, 2, 3, 2
(iii) 1, 5, 7, 9, 2, 4

Solution:

(i) 2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3

How many times does 2 Occur?

2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3

2 occurs 4 times

How many times does 3 Occur?

2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3

3 occurs 6 times

How many times does 4 Occur?

2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3

4 occurs 2 times

How many times does 5 Occur?

2, 3, 4, 3, 2, 4, 3, 2, 3, 5, 3, 2, 5, 3

5 occurs 2 times

3 occurs most frequently, so the mode is 3.

(ii) 4, 1, 4, 2, 4, 2, 3, 2

1 occurs once

2 occurs 3 times

3 occurs once

4 occurs 3 times

The numbers that occur most frequently are 2 and 4

So, the modes are 2 and 4.

Note that if there are two modes in a data, the data is said to be bimodal.

(iii) 1, 5, 7, 9, 2, 4

Each number occurs once, so there is no mode

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