Question
Here are the data sets on two athletes’ swim times for the 100-meter freestyle event in seconds.
Swimmer A: 77 80 83 81 80 80 79
Swimmer B: 75 82 81 86 86 79 71
Which of the following descriptions is true about the data?
(1 point)
Responses
Based on the mode, Swimmer B is faster.
Based on the mode, Swimmer B is faster.
The measures of center for Swimmer A are all the same.
The measures of center for Swimmer A are all the same.
Based on the mean, Swimmer A is faster.
Based on the mean, Swimmer A is faster.
Based on the median, Swimmer B is faster.
Swimmer A: 77 80 83 81 80 80 79
Swimmer B: 75 82 81 86 86 79 71
Which of the following descriptions is true about the data?
(1 point)
Responses
Based on the mode, Swimmer B is faster.
Based on the mode, Swimmer B is faster.
The measures of center for Swimmer A are all the same.
The measures of center for Swimmer A are all the same.
Based on the mean, Swimmer A is faster.
Based on the mean, Swimmer A is faster.
Based on the median, Swimmer B is faster.
Answers
GPT-4o mini
To analyze the swim times for both swimmers, we will calculate the mode, mean, and median for each swimmer and then evaluate the statements.
**Swimmer A Times:**
- Times: 77, 80, 83, 81, 80, 80, 79
- **Mode**: The most frequently occurring time is 80 (it appears 3 times).
- **Mean**:
\[
\text{Mean} = \frac{77 + 80 + 83 + 81 + 80 + 80 + 79}{7} = \frac{560}{7} = 80
\]
- **Median**: The middle value in the ordered list (77, 79, 80, 80, 80, 81, 83) is 80.
**Swimmer B Times:**
- Times: 75, 82, 81, 86, 86, 79, 71
- **Mode**: The most frequently occurring time is 86 (it appears 2 times).
- **Mean**:
\[
\text{Mean} = \frac{75 + 82 + 81 + 86 + 86 + 79 + 71}{7} = \frac{540}{7} \approx 77.14
\]
- **Median**: The middle value in the ordered list (71, 75, 79, 81, 82, 86, 86) is 81.
Now let's go through the statements provided:
1. **Based on the mode, Swimmer B is faster.**
- Mode of A is 80, Mode of B is 86. This is true, but it is not relevant to speed.
2. **The measures of center for Swimmer A are all the same.**
- Mean: 80, Median: 80, Mode: 80. This statement is true.
3. **Based on the mean, Swimmer A is faster.**
- Mean A: 80, Mean B: approx. 77.14. This statement is true.
4. **Based on the median, Swimmer B is faster.**
- Median A: 80, Median B: 81. This is false.
Based on this analysis:
- The correct description(s) are:
- "The measures of center for Swimmer A are all the same."
- "Based on the mean, Swimmer A is faster."
So, at least the statement "Based on the mean, Swimmer A is faster" is true. If needing to choose one, that would be the best option.
**Swimmer A Times:**
- Times: 77, 80, 83, 81, 80, 80, 79
- **Mode**: The most frequently occurring time is 80 (it appears 3 times).
- **Mean**:
\[
\text{Mean} = \frac{77 + 80 + 83 + 81 + 80 + 80 + 79}{7} = \frac{560}{7} = 80
\]
- **Median**: The middle value in the ordered list (77, 79, 80, 80, 80, 81, 83) is 80.
**Swimmer B Times:**
- Times: 75, 82, 81, 86, 86, 79, 71
- **Mode**: The most frequently occurring time is 86 (it appears 2 times).
- **Mean**:
\[
\text{Mean} = \frac{75 + 82 + 81 + 86 + 86 + 79 + 71}{7} = \frac{540}{7} \approx 77.14
\]
- **Median**: The middle value in the ordered list (71, 75, 79, 81, 82, 86, 86) is 81.
Now let's go through the statements provided:
1. **Based on the mode, Swimmer B is faster.**
- Mode of A is 80, Mode of B is 86. This is true, but it is not relevant to speed.
2. **The measures of center for Swimmer A are all the same.**
- Mean: 80, Median: 80, Mode: 80. This statement is true.
3. **Based on the mean, Swimmer A is faster.**
- Mean A: 80, Mean B: approx. 77.14. This statement is true.
4. **Based on the median, Swimmer B is faster.**
- Median A: 80, Median B: 81. This is false.
Based on this analysis:
- The correct description(s) are:
- "The measures of center for Swimmer A are all the same."
- "Based on the mean, Swimmer A is faster."
So, at least the statement "Based on the mean, Swimmer A is faster" is true. If needing to choose one, that would be the best option.