Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 11

The heights of 15 boys from years 1, 2, 3, 4, and 6 are recorded. The heights are shown in the following scatter graph. Use a line of best fit to estimate the height of a boy in year 5.

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Video Transcript

The heights of 15 boys from years one, two, three, four, and six are recorded. The heights are shown in the following scatter graph. Use a line of best fit to estimate the height of a boy in year five.

Before starting any graph question, it is important to understand the labelling on both of the axes. On the 𝑥-axis, we have the year groups from one to six. These are discrete numbers, as the year group must take one of these exact values. For example, you couldn’t be in a year 1.5. As a result, we don’t need to worry about each little square on the 𝑥-axis.

The 𝑦-axis represents the height of each boy in centimetres. Height is a continuous variable. Therefore, we do need to work out what each little square on the 𝑦-axis represents. We can see that 10 squares represents 10 centimetres. Dividing both of these by 10 tells us that one square is equal to one centimetre on the 𝑦-axis.

A scatter graph can show three types of correlation: positive correlation, negative correlation, and no correlation. In this question, the graph shows a positive correlation, as the points generally slope upwards from left to right. We can therefore say that the higher the year group, the taller the boy. The age or year group of a child and their height have a positive correlation. As one increases, so does the other.

In order to answer this question, we need to draw a line of best fit. A line of best fit needs to have roughly the same number of points above and below the line. It also needs to have points above and below the line at the top and bottom of the graph.

The line of best fit could look something like this. Please note that this line must be drawn with a ruler and that everybody’s lines will be slightly different. As a result, there will be a small margin for error in terms of our final answer.

We were asked to estimate the height of a boy in year five. Firstly, we draw a line vertically upwards from five to our line of best fit. We then draw a horizontal line across to the 𝑦-axis. In our case, this gives us an answer of 140 centimetres.

The estimate for the height of a boy in year five is 140 centimetres. If your answer was slightly above or below this number, remember that one square on the 𝑦-axis was equal to one centimetre.

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