Application of Number

Level 2

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Mode - Tutorial 3

The mode is the Most Popular of a set of numbers. The most popular is useful in analysing data.

E.g.

• most popular subject,
• most common price for a CD,
• most common test score.

To find the mode:

E.g. 1

If we wanted to find the mode of this set of numbers.

The data:

10, 12, 12, 10, 9, 11, 11, 13, 11, 9, 8

1. First we add order the numbers.

8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13

HINT: Always count the number of numbers before and after ordering, just to make sure that you haven't missed any out. In this case we have 11 numbers.

2. Find the most popular number.

8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13

In this case the mode was 11.

E.g. 2

If we wanted to find the mode exam score of students.

The data:

90, 89, 90, 85, 90, 86, 89, 90, 85, 90, 84, 83

1. First we order the numbers.

83, 84, 85, 85, 86, 89, 89, 90, 90, 90, 90, 90

2. Then we find the most popular number.

83, 84, 85, 85, 86, 89, 89, 90, 90, 90, 90, 90

The mode was 90.

Notice how the highest score was also 90. There may be a reason for this and using statistics can help solve problems. It may be that nearly all students got stuck on the same question and that is why no one got more than 90.

NOTE

Sometimes there isn't a mode, because there isn't a particular number that is more popular than the others.

E.g. 3

3, 5, 4, 7, 6, 1, 2

In order

1, 2, 3, 4, 5, 6, 7

No mode!

Sometimes there is more than one number that is the mode.

E.g. 4

4, 5, 6, 4, 5, 8, 7, 3

In order

3, 4, 4, 5, 5, 6, 7, 8

Mode is 4 and 5.

To find the mode

To practise finding the mode try this assessment.

Then go on to the next tutorial.

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