Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 19

The table shows data about people running a marathon. Make three comparisons of males and females at the marathon. Use the headings given. Proportion of runners, Average height, Apread of heights.

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Video Transcript

The table shows data about people running a marathon. Make three comparisons of males and females at the marathon. Use the headings given. Proportion of runners, average height, and spread of heights.

The first part of the question asks us to compare the proportion of runners. We do this by looking at the percentage column in the table. 51 percent of the runners were female and 49 percent were male. Therefore, the ratio of females to males is 51 to 49. Out of every 100 runners, 51 are female and 49 are male. We can therefore conclude that in terms of the proportion of runners, there are slightly more female than male runners.

The second part of the question asks us to compare the average height of males and females. We do this by looking at the mean height column. The mean or average height of females running the marathon was 166.2 centimeters. The average height of the males was 175.8 centimeters. 175.8 minus 166.2 is equal to 9.6. This means that on average, the male runners are 9.6 centimeters taller than the female runners. The average height for the males is greater than the average height for the females.

Finally, we are asked to compare the spread of the heights of males and females. We do this by looking at the height range column. The range of heights is calculated by subtracting the shortest person’s height from the tallest person’s height. For females, this was equal to 12 centimeters. And for males, this was equal to 25 centimeters. 25 is greater than 12. Therefore, the height range for males was greater than the height range for females. We can therefore conclude that the heights of the males were more spread out than the females.

Based on the data in the table, we have concluded that there were slightly more females than males, that males on average were taller than females, and that the height of the males was more spread out than the height of the females.

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