Lesson 3, Topic 3
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# The Median

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The median of a set of values or data is the middle value when the data is arranged in order of magnitude or size.

### Example 1:

Find the median of: 12, 34, 13, 22, 27, 40, 8, 31, 17

Solution:

Arrange the numbers in order of increasing size

8, 12, 13, 17, 22, 27, 31, 34, 40.

There are nine numbers.

8, 12, 13, 17, 22, 27, 31, 34, 40.

The 5th number is in the middle. The 5th number is 22.

Median = 22

Note that the result is the same if the numbers are arranged in order of decreasing size.
40, 34, 31, 27, 22, 17, 13, 12, 8

### Example 2:

Find the median of these numbers:
13, 15, 14, 12, 13, 15, 16, 11, 12, 14

Solution:

Arranging the numbers in order to magnitude starting with the smallest value:

11, 12, 12, 13, 13, 14, 14, 15, 15, 16

⇒ $$\scriptsize \underset{(4 \: values)}{11, 12, 12, 13} \; \underset{(middle \: numbers)}{13,14} \; \underset{(4 \: values)}{14, 15, 15, 16}$$

In this example, we have even number of values, 10 there is no middle number. To obtain the median, we add the two middle numbers and the divide the result by 2.

Median = $$\\ \frac{sum\:of\:the\:two\:middle\:numbers}{2} \\ = \frac{13 \: + \: 14}{2} \\ = \scriptsize13 \frac{1}{2} \: or \: 13.5$$

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