Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 23

The table shows information about the number of boys and girls in three different year groups at a primary school. The graph shows Jamal’s attempt to draw a composite bar graph for this information. Write down three mistakes Jamal has made.

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Video Transcript

The table shows information about the number of boys and girls in three different year groups at a primary school. The graph shows Jamal’s attempt to draw a composite bar graph for this information. Write down three mistakes Jamal has made.

The table tells us that in year four, there were 19 boys and 11 girls. In year five, there were 10 boys and 18 girls. And in year six, there were 12 boys and 19 girls. When drawing any bar graph, it is important that we have a title and that our axes are labelled correctly. Our graph does indeed have a title, number of boys and girls in years four, five, and six. The 𝑥-axis is also labelled correctly. It is the year groups four, five, and six.

The 𝑦-axis, initially, also appears to be labelled correctly, as it says number of students. And it goes from zero to 35. However, there is an issue on the 𝑦-axis. Each interval needs to be the same. Each one of the intervals of 10 squares represents adding five, apart from the first one where it represents adding 10. The first mistake that Jamal made when drawing a composite bar graph is that the 𝑦-axis scale is not linear. It does not increase at constant intervals.

A composite bar graph means that there will be at least two pieces of information on each bar. In this question, the first bar represents the boys and girls in year four. The second bar, the boys and girls in year five. And the third bar, the boys and girls in year six. In Jamal’s graph, there is no key. So there is no way of distinguishing whether the grey part or the white part represents boys or girls. His second mistake is that there is no key to label which section is boys and girls.

Let’s assume that the grey section represents the boys and the white section represents the girls. We can now work out how many people each of the sections represents. In year four, there were 19 boys and 11 girls. 19 plus 11 is equal to 30. Therefore, that height of the bar should be 30. This is correct; there are 19 boys and 11 girls represented in the first bar. In year five, there were 10 boys and 18 girls. 10 plus 18 is equal to 28. Therefore, the height of the bar should be 28. This final bit is correct, as the bar does have a height of 28.

However, this time, the grey section has a height of 18 and the white section has a height of 10. The girls’ and boys’ sections have been swapped over. The girls are now in grey and the boys are in white. Jamal’s third mistake is that the sections for year five appear to have been reversed for the boys and girls.

There were three key mistakes on Jamal’s composite bar graph. One, the 𝑦-axis scale was not linear. Two, there was no key to label which section is boys and girls. And three, the sections for year five have been reversed.

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