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Sarah’s fitness class has been working on improving their burpee performance. The class average was determined to be 10 burpees per minute.
Over 10 days, Sarah tracked how many burpees she could do in one session and how long it took her.
The tables below show her results:
| Day | Burpees | Time taken |
|---|---|---|
| 1 | 8 | 1 min |
| 2 | 9 | 1 min 5 s |
| 3 | 9 | 1 min |
| 4 | 10 | 1 min 5 s |
| 5 | 11 | 1 min 10 s |
| Day | Burpees | Time taken |
|---|---|---|
| 6 | 12 | 1 min 15 s |
| 7 | 12 | 1 min 10 s |
| 8 | 13 | 1 min 15 s |
| 9 | 14 | 1 min 20 s |
| 10 | 15 | 1 min 25 s |
a) Complete the tables by calculating Sarah’s burpees per minute for each day, rounding to the nearest decimal.
b) Calculate the mean of the values you found in (a). How does Sarah’s mean compare to her class average?
c) Which type of graph would be most appropriate to show Sarah’s improvement over time? Create a suitable graph with appropriate labels.
d) Based on the trend in Sarah’s performance, predict how many burpees she might be able to do in one minute on Day 15 of her training.
a) Completed tables with burpees per minute:
| Day | Burpees | Time taken | Burpees/min |
|---|---|---|---|
| 1 | 8 | 1 min | 8.0 |
| 2 | 9 | 1 min 5 s | 8.3 |
| 3 | 9 | 1 min | 9.0 |
| 4 | 10 | 1 min 5 s | 9.2 |
| 5 | 11 | 1 min 10 s | 9.4 |
| Day | Burpees | Time taken | Burpees/min |
|---|---|---|---|
| 6 | 12 | 1 min 15 s | 9.6 |
| 7 | 12 | 1 min 10 s | 10.3 |
| 8 | 13 | 1 min 15 s | 10.4 |
| 9 | 14 | 1 min 20 s | 10.5 |
| 10 | 15 | 1 min 25 s | 10.6 |
Calculation example (Day 2): (9 burpees ÷ 65 seconds) × 60 seconds/minute ≈ 8.3 burpees/minute
b) Sarah’s mean burpees per minute:
(8.0 + 8.3 + 9.0 + 9.2 + 9.4 + 9.6 + 10.3 + 10.4 + 10.5 + 10.6) ÷ 10 = 95.3 ÷ 10 = 9.53
Sarah’s mean of 9.5 burpees per minute (rounded to one decimal) is slightly lower than the class average of 10 burpees per minute.
c) A line graph would be most appropriate to show Sarah’s improvement over time. It allows us to see the trend and rate of improvement clearly. (See attached graph)
d) To predict Sarah’s performance on Day 15, we can observe the trend:
– She started at 8.0 burpees/minute on Day 1
– She reached 10.6 burpees/minute on Day 10
– This is an increase of 2.6 burpees/minute over 9 days, or about 0.29 burpees/minute per day
If this trend continues:
– Over 5 more days, she might improve by: 5 × 0.29 = 1.45 burpees/minute
– Predicted performance on Day 15: 10.6 + 1.45 ≈ 12.05 burpees/minute
Therefore, Sarah might be able to do about 12 burpees in one minute on Day 15 of her training.
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