# Ironman Athletes: A Case Study

b) The remaining 80% of the final grade is determined by how well a person does in the test and the final exam. Plussage is used to decide whether the exam counts for 60% or 70% (and the test counts for 10% or 20%) of the final grade. Whichever of these produces the highest mark is used.

a) The total times is a numeric, continuous variable therefore a dot plot and a box plot are used. The modality of the data is unimodal (one peak) at 339 minutes. 50% of the Ironman athletes finish the race between 305.6 and 370.7 minutes. Although, there is a large standard deviation of 48.9. This entails that there is a large distance between the mean and the points, hence a

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The data set was displayed as a scatter plot, as two numeric variables were being compared. It showed a strong, non-linear trend between the transition and total times. As X (transition) increased so did Y (total times). Therefore, the athletes who finished the race early had less transition versus those who finished the race late had a higher transition. There was a positive association with a correlation of 0.8. The high correlation shows how closely related the two variables are. The majority of the athletes were clustered the bottom left corner of the scatter plot. Although, there were several unusually high data points, particularly with those finishing the race late and also having a high transition. The graph should be analysed in subgroups, separating the male from the female athletes would show whether the subgroups behave

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Although there are only 39 female athletes. There is one cluster in the data set between 290 and 320 in total times. The male athletes had a faster total time mean of 312.4. There was also more than three times the number of male athletes (n=130) compared to females. Males had a smaller standard deviation of 20.4. This meant the spread was less for the male athlete’s compared to the females, possibly due to fitness level. The male graph was bimodal which peaked at both 385 and 312 in total times.

For the 4-6 transition data set, female athletes had a mean of 367.6 and a standard deviation of 33.5. This subset had the highest number of female athletes at 58. There are two unusually high/low points in this graph, both had reasonable transition times but had high total times (seen as the last two points on the dot plot). The male athletes had a faster total time mean of 340.1. There were also more male athletes (n=198) compared to females. Males had a larger standard deviation of 32.2. Again, possibly due to the sample size. The male graph was unimodal, only peaking once at the mean