To analyze the data of the two swimmers, we will calculate the mean, mode, and median for both Swimmer A and Swimmer B.
Swimmer A's times: 77, 80, 83, 81, 80, 80, 79
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Mean for Swimmer A: \[ \text{Mean} = \frac{77 + 80 + 83 + 81 + 80 + 80 + 79}{7} = \frac{560}{7} = 80 \]
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Mode for Swimmer A: The time that occurs most frequently is 80 (it appears three times).
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Median for Swimmer A: Arranging the times in order: 77, 79, 80, 80, 80, 81, 83 The median is the middle value: 80.
Swimmer B's times: 75, 82, 81, 86, 86, 79, 71
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Mean for Swimmer B: \[ \text{Mean} = \frac{75 + 82 + 81 + 86 + 86 + 79 + 71}{7} = \frac{570}{7} \approx 81.43 \]
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Mode for Swimmer B: The time that occurs most frequently is 86 (it appears twice).
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Median for Swimmer B: Arranging the times in order: 71, 75, 79, 81, 82, 86, 86 The median is the middle value: 81.
Now we can compare based on the calculations:
- Mean: Swimmer A = 80, Swimmer B ≈ 81.43 → Swimmer A is faster based on mean.
- Mode: Swimmer A (80) vs. Swimmer B (86) → Based on mode, Swimmer B is faster.
- Median: Swimmer A (80) vs. Swimmer B (81) → Based on median, Swimmer B is faster.
Reviewing the options:
- Based on the mean, Swimmer A is faster. (True)
- Based on the mode, Swimmer B is faster. (True)
- The measures of center for Swimmer A are all the same. (False, they are all 80 and thus equal, but the other swimmer's measures differ.)
- Based on the median, Swimmer B is faster. (True)
Since all options are at least partially correct, let's summarize:
- Swimmer A is faster based on the mean.
- Swimmer B is faster based on the mode and median.
The true statement among the answers is: Based on the mean, Swimmer A is faster.