Question

Mr Laing is in the business of selling triathlon gear. He decided to sponsor 10 triathletes in order to get his brand noticed. After the Ironman 70,3 race he asked you to conduct a study on the finishing times (in minutes) for these 10 triathletes.

\begin{array}{|l|l|}
\hline \text { Athlete } & \text { Finishing time (in minutes) } \\
\hline \text { AJ Snyman } & 320 \\
\hline \text { N Els } & 415 \\
\hline \text { M Paton } & 402 \\
\hline \text { G Dombo } & 360 \\
\hline \text { J Thorpe } & 300 \\
\hline \text { D Radia } & 399 \\
\hline \text { D Breda } & 356 \\
\hline \text { J Young } & 298 \\
\hline \text { M Honiball } & 306 \\
\hline \text { T Nomvete } & 367 \\
\hline
\end{array}

1. Calculate the mean of the finishing times of the triathletes.
2. What is the mode of the finishing times of the triathletes?
3. Calculate the median of the finishing times of the triathletes.
4. Calculate the lower quartile of the above finishing times of the triathletes.
5. Calculate the upper quartile of the finishing times of the triathletes.
6. Interpret the upper quartile calculated in question 5 .
7. Calculate the range of the finishing times of the triathlon.
8. Calculate the standard deviation if \(\sum(x-\bar{x})^{2}=17742,10 .\)
9. Based on your answer in Q8, what suggestions would you make to Mr Laing regarding his marketing strategy?

Mr Laing is interested in finding out more about the age groups of the triathletes. You conducted a study on the same group of 10 triathletes and recorded their ages, summarised in the frequency table below:

\begin{array}{|l|l|l|}
\hline \text { Age (years) } & \text { Class boundaries } & \text { Frequency } \\
\hline 20-29 & 19,5-29,5 & 2 \\
\hline 30-39 & 29,5-39,5 & 4 \\
\hline 40-49 & 39,5-49,5 & 2 \\
\hline 50-59 & 49,5-59,5 & 1 \\
\hline 60-69 & 59,5-69,5 & 1 \\
\hline
\end{array}

10. Mr Laing has attempted to construct a histogram and requests you to assist to indicate which values using percentage frequency would be correct on the histogram below as well in labelling the axes.

11. What is the percentage of triathletes in the \(30-39\) age group?