Leaving Cert Mathematics Statistics & Data: The King of the Hill triathlon r

Question

The King of the Hill triathlon race in Kinsale consists of a 750 metre swim, followed by a 20 kilometre cycle, followed by a 5 kilometre run.

Maire is analysing data from the race, using statistical software. She has a data file with each competitor's time for each part of the race, along with various other details of the competitors.

Maire produces histograms of the times for the three events. Here are the three histograms.

(a) Use the histograms to complete the following sentences:

(i) The event that, on average, takes longest to complete is the ______________.

(ii) In all three histograms, the times are grouped into intervals of _____________ minutes.

(iii) The time of the fastest person in the swim was between _________ and _______ minutes.

(iv) The median time for the run is approximately __________ minutes.

(v) The event in which the times are most spread out is the ______________.

(b) Maire is interested in the relationship between the athletes' performance in the run and in the cycle. She produces the following scatter diagram.

Run vs. Cycle

(i) The correlation coefficient between the times for these two events is one of the numbers below. Write the letter corresponding to the correct answer in the box.

A. 0.95
B. 0.77
C. 0.13
D. -0.13
E. -0.77
F. -0.95

(ii) Frank was the slowest person in the run. How many people took longer to complete the cycle than Frank did?

Answer: ______________.

(iii) Brian did not enter this race. Suppose that he had, and that he completed the cycle in 52 minutes and the run in 18 minutes. Explain why this performance would have been very unusual.

(e) Maire knows already that the male athletes tend to be slightly faster than the female athletes. She also knows that athletes can get slower as they get older. She thinks that male athletes in their forties might be about the same as female athletes in their thirties. She decides to draw a back-to-back stem-and-leaf diagram of the times of these two groups for the swim. There were 28 females in their thirties, and 32 males in their forties. Here is the diagram:

Female, 30 – 39 years
4 1 9
1 0
5 3 6 4 7 8
9 6 3 1 0 0
0 2 1 2 1
4 2 3 2
4 22
0 25
8 24
5 26
2 27
6 29

Key: | 14 | 9 means 14.9 minutes.

(i) Describe what differences, if any, there are between the two distributions above.

(ii) Maire drew the diagram because she thought that these two groups would be about the same. Do you think that the diagram would cause Maire to confirm her belief or change it? Give reasons for your answer.

The King of the Hill triathlon race in Kinsale consists of a 750 metre swim, followed by a 20 kilometre cycle, followed by a 5 kilometre run - Leaving Cert Mathematics - Question 7 - 2013

Worked Solution & Example Answer:The King of the Hill triathlon race in Kinsale consists of a 750 metre swim, followed by a 20 kilometre cycle, followed by a 5 kilometre run - Leaving Cert Mathematics - Question 7 - 2013

Use the histograms to complete the following sentences: (i) The event that, on average, takes longest to complete is the __________.

(ii) In all three histograms, the times are grouped into intervals of _____________ minutes.

(iii) The time of the fastest person in the swim was between ___ and _ minutes.

(iv) The median time for the run is approximately __________ minutes.

(v) The event in which the times are most spread out is the ______________.

(b)(i) The correlation coefficient between the times for these two events is one of the numbers below. Write the letter corresponding to the correct answer in the box.

(ii) Frank was the slowest person in the run. How many people took longer to complete the cycle than Frank did?

(iii) Brian did not enter this race. Suppose that he had, and that he completed the cycle in 52 minutes and the run in 18 minutes. Explain why this performance would have been very unusual.

(e)(i) Describe what differences, if any, there are between the two distributions above.

(ii) Maire drew the diagram because she thought that these two groups would be about the same. Do you think that the diagram would cause Maire to confirm her belief or change it? Give reasons for your answer.

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