Analysing data - EduqasMedian

An average is the typical value within a set of data. There are three forms of average: mean, median and mode. It is important to know what they are and which form of average to choose.

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Median

Explore the refreshed revision guide for GCSE Maths: Median, with step-by-step slideshows, quizzes, practice exam questions, and more!

The median average is the middle number in a set of data, when the data has been sorted into size order.

If there is an odd number of items of data, there will be one number in the middle.

If there is an even number of items of data, there will be two numbers in the middle. The median is the number that is half way between these two numbers.

To find the median, put all numbers into ascending order and work into the middle by crossing off numbers at each end.

If there are a lot of items of data, add 1 to the number of items of data and then divide by 2 to find which item of data will be the median. This works when it is an odd number but when it is an even number you will get a decimal answer such as 7.5. The median will be halfway between the 7th and 8th items.

Example

7 babies weigh the following amounts:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Find the median weight of the babies.

The numbers are already in order. Find the median amount by finding the middle number.

Cross off the first and last item of data (the items in bold):

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Repeat until you reach the middle:

3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg

3.4 kg, 3.5 kg, 3.5 kg

3.5 kg

The median weight of these babies is 3.5 kg.

Another method is to find which item of data is the median.

There are 7 numbers, so adding 1 to 7 then dividing by 2 gives: \(\frac{7+1}{2}=\frac{8}{2} = 4\), so the median value is the 4th number in the list:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

The median weight of these babies is 3.5 kg.

Notice that this is the median value as, in ascending order, there are 3 values before it and 3 values after that central value.

If another baby was born that weighed 3 kg then the list would change to this:

2.5 kg, 3 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Now there are 2 items of data in the middle, so the median is half way between 3.4 kg and 3.5 kg, which is 3.45 kg. Again, an alternative method would be to add 1 to 8 then divide by 2, giving: \(\frac{8+1}{2}=\frac{9}{2} = 4.5\), so the median values are the 4th and 5th numbers in the list:

The median weight of these 8 babies is 3.45 kg.

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