In the sport of heptathlon, athletes compete in seven events.
These events are the 100 m hurdles, high jump, shot-put, javelin, 200 m run, 800 m run and long jump.
Fifteen female athletes competed to qualify for the heptathlon at the Olympic Games.
Their results for three of the heptathlon events – high jump, shot-put and javelin – are shown in Table 1.
- Write down the number of numerical variables in Table 1. (1 mark)
- Complete Table 2 below by calculating the mean height jumped for the high jump, in metres, by the 15 athletes. Write your answer in the space provided in the table. (1 mark)
- In shot-put, athletes throw a heavy spherical ball (a shot) as far as they can.
Athlete number six, Jamilia, threw the shot 14.50 m.
Calculate Jamilia's standardised score (`z`).
Round your answer to one decimal place. (1 mark) - In the qualifying competition, the heights jumped in the high jump are expected to be approximately normally distributed.
Chara's jump in this competition would give her a standardised score of `z = –1.0`
Use the 68–95–99.7% rule to calculate the percentage of athletes who would be expected to jump higher than Chara in the qualifying competition. (1 mark)
- The boxplot below was constructed to show the distribution of high jump heights for all 15 athletes in the qualifying competition.
Explain why the boxplot has no whisker at its upper end. (1 mark) - For the javelin qualifying competition (refer to Table 1), another boxplot is used to display the distribution of athlete's results.
An athlete whose result is displayed as an outlier at the upper end of the plot is considered to be a potential medal winner in the event.
What is the minimum distance that an athlete needs to throw the javelin to be considered a potential medal winner? (2 marks)