Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 1 • Question 20

Some grandparents took their grandchildren to the swimming pool. The ages of the people present in the swimming pool are shown in the grid. Simon wants to find the average age of the people in the swimming pool. Which average is the most appropriate? Tick the correct box. Is it the median, mean, or mode? And give a single reason for why each of the other two averages would not be appropriate.

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Video Transcript

Some grandparents took their grandchildren to the swimming pool. The ages of the people present in the swimming pool are shown in the grid. Simon wants to find the average age of the people in the swimming pool. Which average is the most appropriate? Tick the correct box. Is it the median, mean, or mode? And give a single reason for why each of the other two averages would not be appropriate.

Let’s recap on our understanding of the three measures of average and their benefits. The median is the middle value when the list is in order. The median tends to be less affected by outliers; those are extreme values that don’t fit the pattern.

Let’s list the ages of the people present in the swimming pool in order of size. It’s three, four, five, six, seven, 58, 61, 62, and 70. One way of finding the median — the middle value — is to start crossing off values from the outside in. So we cross off three and 70. We cross off four and 62, five and 61, and six and 58. And we’re left with seven.

The median age then of the people present in the swimming pool is seven. This isn’t usually representative of the data given. We are not going to use the median then. Because the median is only seven, it ignores all the ages of the grandparents.

What about the mean? The mean is found by adding the numbers together and dividing by how many we have. The mean is really useful because it takes all data into account. And we saw that the median didn’t really do that. We ended up with an unusually low value, giving the ages of the grandparents. So the mean might be a good option here.

Let’s briefly consider the mode. The mode is the most common value. It is the value that occurs the most. There is no mode for this set of data. So that means we wouldn’t choose that for a measure of average.

This means that we are going to need to use the mean. And the reasons that are most appropriate are well firstly, the median is seven, which ignores all of the ages of the grandparents and secondly, no age occurs more frequently than the other. There’s no mode. So we can’t use it.

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