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Median Average (Mathematics Lesson)

What Is Median Average?

The median average (or median) is the middle number in a set of numbers that has been arranged in order.

How to Find the Median Average

Question: What is the median of 8, -15, 14, 54, and 8?

Step 1
Sort the list from smallest to largest.
Step 2
Select the middle number. That's the median.

Answer: 14

How to Find the Median Average with an Even Amount of Numbers

When a set has an odd amount of numbers, the median is easily found. (It's the one in the middle with an equal amount of numbers either side of it). However, if the amount of numbers is even, finding the median is a little trickier as there is no middle number. For example:

Question: What is the median of 16, 9, 24, and 33?

Step 1
Sort the list from smallest to largest.
Step 2
Select the middle 2 numbers.
Step 3
Add those 2 numbers and divide by 2. That's the median.



Answer: 20
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Top Tip

FINDING THE MIDDLE NUMBER QUICKLY

To find the middle number quickly, add 1 to the amount of numbers in the set and then divide by 2. For example, if there are 9 numbers in the set, add 1 (giving you 10), then divide by 2 (giving you 5). The 5th number in the set is the median.

With a set with an even amount of numbers, do the same. For example, if there are 10 numbers in the set, add 1 (giving you 11), then divide by 2 (giving you 5.5). This means we have to take the 5th and 6th numbers in the set. (You then have to add them and divide by 2 for your median.

This tip is useful with large sets of numbers. For example, if there are 75 numbers in the set, add 1 (giving you 76), then divide by 2 (giving you 38). This means we have to take the 5th and 6th numbers in the set. The 38th number in the set is the median.
WHEN IS THE MEDIAN USEFUL?

Median is useful when the set has numbers outside the expected range which would skew the mean.

For example, if we were to look at the average age of a school class, the mean will be skewed by the age of the teacher. The median, however, would give us a better idea of the age of the children.

Read about mean average.
Read about mode average.

ENSURE YOUR SET IS IN ORDER

Remember, always sort the list of numbers before you look for the median. An unsorted or incorrectly sorted list will very likely give you the wrong answer.