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Measures of average

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The mode

The mode is the value that occurs most often.

The mode is the only average that can have more than one value.

When finding the mode, it helps to order the numbers first.

Finding the mode

Question

Find the mode of each of the following sets of numbers:

a) 3, 7, 1, 3, 4, 8, 3
b) 2, 7, 2, 1, 4, 7, 3

Answer

a) Start by placing the numbers in order:
1, 3, 3, 3, 4, 7, 8
The number 3 occurs most often so the mode is 3.

b) Start by placing the numbers in order:
1, 2, 2, 3, 4, 7, 7
The numbers 2 and 7 occur more often than all other numbers so the modes are 2 and 7.

Example

In this frequency table, the mode is the value with the highest frequency:

Shoe size 5 6 7 8 9
Frequency 2 5 11 4 1

In this example the modal shoe size is 7, because more people take size 7 than any other size.

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