A triathlon is an endurance race consisting of swimming 3.8 km, cycling 180 km, and running 42.2 km. Athletes compete for the fastest overall time, completing each segment in that order. The following table shows the finish time of 3 athletes in each segment.
- (i) What is a suitable representation of this data — a stacked bar chart or a 100% stacked bar chart? Why do you think so?
- (ii) Suppose a 100% stacked bar chart is drawn. Which of the following question(s) can be answered by looking at just that chart?
(a) Who finished the race first?
(b) Approximately what fraction of their race time did Athlete 1 spend cycling?
(c) Which athlete took the longest for running?
Answer: (i) A stacked bar chart: the race is decided by total time, which a stacked bar shows as the bar’s length, along with each segment. (ii) From a 100% chart only (b) can be answered (cycling ≈ 53%, just over half of Athlete 1’s time); (a) and (c) need actual times.
Step-by-step solution
Given: Finish time of three athletes in each segment of a triathlon race (values in hh : mm)
| Swimming | Cycling | Running | |
|---|---|---|---|
| Athlete 1 | 01:08 | 05:00 | 03:15 |
| Athlete 2 | 01:05 | 05:10 | 03:35 |
| Athlete 3 | 01:22 | 05:55 | 03:50 |
Idea: Ask whether the question is about amounts (total time, time for running) or about shares of each athlete’s own time. Stacked bars keep the amounts; 100% bars keep only shares.
(i) What is a suitable representation of this data — a stacked bar chart or a 100% stacked bar chart? Why do you think so?
- Totals: Athlete 1 = 1:08 + 5:00 + 3:15 = 9:23 (563 min); Athlete 2 = 9:50 (590 min); Athlete 3 = 11:07 (667 min). The winner is decided by total time, so a stacked bar chart is suitable: its bar lengths show the totals and the pieces show each segment. A 100% chart would make all bars equal and hide who was fastest.1 mark
Stacked bar chart
(ii) Suppose a 100% stacked bar chart is drawn. Which of the following question(s) can be answered by looking at just that chart?
(a) Who finished the race first?
(b) Approximately what fraction of their race time did Athlete 1 spend cycling?
(c) Which athlete took the longest for running?
- (a) No. All bars have the same length in a 100% chart, so total times (563, 590, 667 min) are hidden. (From the table, Athlete 1 finished first.)1 mark
- (b) Yes. It is a share of Athlete 1’s own time: 300563 ≈ 53%, just over half.1 mark
- (c) No. The chart shows running as a share: about 35%, 36% and 34%, which would wrongly suggest Athlete 2. In fact Athlete 3 ran longest (3:50). Shares cannot compare actual times.1 mark
Only (b): Athlete 1 cycled for about 53% (just over half) of the race time
(i) A stacked bar chart, because the race is won on total time, which the bar lengths show (Athlete 1: 9 h 23 min, Athlete 2: 9 h 50 min, Athlete 3: 11 h 7 min). (ii) Only (b) can be answered from a 100% chart: Athlete 1 spent about 53% (just over half) of the race cycling.
Check: Minutes: 68 + 300 + 195 = 563, 65 + 310 + 215 = 590, 82 + 355 + 230 = 667 ✓. Running shares: 195563 ≈ 34.6%, 215590 ≈ 36.4%, 230667 ≈ 34.5%.
Answer to write in the exam
(i)
Totals: 563 min, 590 min, 667 min
Race decided by total time
∴ Stacked bar chart (shows totals and segments)
(ii)
(a) totals hidden in a 100% chart ⇒ cannot answer
(b) 300563 ≈ 0.53 ⇒ can answer: just over half
(c) running shares 35%, 36%, 34% do not give times ⇒ cannot answer
∴ Only (b)
Common mistakes that cost marks
- Adding hh:mm values as decimals (for example 1.08 + 5.00 + 3.15 = 9.23 h). Convert to minutes first.
- Saying a 100% chart shows who finished first.
- In (c), picking the athlete with the biggest running share; a share is not a time.
How this can come in the exam
MCQ (1 mark)
Which question can be answered from a 100% stacked bar chart of three students’ study time split by subject?
- Who studied the most hours?
- What fraction of her time did Asha spend on maths?
- Who spent the most hours on science?
- What was the total study time?
Show answer
(B) What fraction of her time did Asha spend on maths?
Only a share within one bar can be read from a 100% chart.
Try one yourself
A runner’s race: 40 min uphill, 25 min flat, 15 min downhill. What fraction of the time was uphill?
Show answer
4080 = 12 (50%).
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