# 6.6 Median

The last type of average you will look at briefly is called the median. Put very simply, the median is the middle number in a set of data. The only thing you need to remember is to put the numbers in size order, smallest to largest, before you begin. As this is such a simple process let’s just look at two examples.

## Example: Finding the median 1

Find the median of this data set:

### Method

- 5, 10, 8, 12, 4, 7, 10

Firstly, order the numbers from smallest to largest:

- 4, 5, 7, 8, 10, 10, 12

Now, find the number that is in the middle:

- 4, 5, 7,
**8**, 10, 10, 12

8 is the number in the middle, so the median is 8.

## Example: Finding the median 2

Find the median of this data set:

### Method

- 24, 30, 28, 40, 35, 20, 49, 38

Again, you firstly need to order the numbers:

- 20, 24, 28, 30, 35, 38, 40, 49

And then find the one in the middle:

- 20, 24, 28,
**30**,**35**, 38, 40, 49

In this example there are actually two numbers that are in the middle, you therefore find the middle of these two numbers by adding them together and then halving the answer:

- (30 + 35) ÷ 2 = 32.5

The median for this set of data is 32.5.

If you want to see some more examples, or try some for yourself, use the link below:

https://www.mathsisfun.com/ median.html [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

Well done! You have now learned all you need to know about mean, median and range. The final part of this section, before the end-of-session quiz, looks at probability.

## Summary

In this section you have learned:

- that there are different types of averages that can be used when working with a set of data – range, mean, median and mode
- range is the difference between the largest data value and the smallest data value and is useful for comparing how consistently someone or something performs
- mean is what is commonly referred to when talking about the average of a data set
- how to find the mean from both a single data set and also a set of grouped data
- formulas and inverse operations to calculate missing data when given the mean of a data set
- what the median of a data set is and how to find it for a given set of data.