Video: GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 14

GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 14


Video Transcript

Kyla has a list of numbers displayed in the grid. Kyla says, “The median is the middle number, so the median of these numbers is 27.” Kyla is incorrect.

a) Explain why Kyla is wrong.

The median is the middle number, so at first glance it does indeed look like Kyla might be correct. However, she does have the definition of the median slightly wrong. In fact, the median number is the middle number when they are in order. These numbers are not in order of size. So we’ll need to do that before being able to calculate the median.

Once we’ve put these numbers in order of size, we can work our way into the middle number from the outside by crossing them off one at a time. When we do so, we see that the median number is in fact 21. Kyla is wrong because the median is the middle number in an ordered list, and her list is not in order.

Part two) Calculate the range of Kyla’s list of numbers.

The range is the difference between the largest value and the smallest value in the list. Once the list is in order, these are really easy to spot. The largest value is 32, and the smallest is seven. The difference between 32 and seven is 25. So the range of the list of numbers is 25.

Part c) Calculate the mean of Kyla’s numbers.

To calculate the mean, which is a measure of average, we add the numbers together and divide them by the total amount of numbers that there are. The sum total of the numbers is 180, and there are a total of one, two, three, four, five, six, seven, eight, nine numbers in the grid. The mean is therefore found by dividing 180 by nine. 18 divided by nine is two, so 180 divided by nine is 20. The mean of Kyla’s numbers is 20.

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