Video: AQA GCSE Mathematics Foundation Tier Pack 1 β€’ Paper 2 β€’ Question 5

Calculate the median of the numbers in the grid.


Video Transcript

Calculate the median of the numbers in the grid.

The median is calculated by finding the middle number when the numbers are written in ascending order. We noticed that the numbers in the grid are already written in ascending order from nine up to 25. When we have a small list of numbers like this, one way to find the median is to cross off one number from either end until we reach the middle.

Firstly, we cross off nine and 25. We can then cross off the second nine and 22. Our next step is to cross off the third nine along with 20. As we had an even number of numbers in the grid, there were eight, we will end up with two middle numbers. If these two numbers are different, as in this case, the median is halfway between the two numbers.

If we consider the number line from 15 to 19, we need to find the midpoint or the point that is halfway between these two numbers. To get from 15 to 17, we add two and to get from 19 to 17, we subtract two. Therefore, 17 is the midpoint of 15 and 19. We can, therefore, say that the median of the numbers in the grid is 17.

There is another method we could use which is more useful if we have a large set of data and we don’t want to have to cross off from both ends. The median term is the 𝑛 plus one divided by two term in the list, where 𝑛 is the total number of terms.

In our question, 𝑛 is equal to eight as there were eight numbers in the list. We need to add one to eight and then divide by two. Eight plus one is equal to nine and dividing this by two or halving it gives us 4.5. This means that the median term will be the 4.5th term.

In reality, this means that the median is between the fourth and fifth terms in the list. The fourth term in the list was 15 and the fifth term in the list was 19. Therefore, once again, we can see that the median will be halfway between 15 and 19. This is an alternative method to prove that our median for the eight numbers is equal to 17.

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