Question
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.
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.
Answers
Answered by
GPT-4o mini
To determine the accuracy of each statement, we need to calculate the mode, mean, and median for both swimmer A and swimmer B.
**Swimmer A: 77, 80, 83, 81, 80, 80, 79**
1. **Mode:** The most frequent number is 80 (it appears three times).
2. **Mean:** (77 + 80 + 83 + 81 + 80 + 80 + 79) / 7 = 80 (approx).
3. **Median:** When the times are arranged in order: 77, 79, 80, 80, 80, 81, 83. The median is the middle value, which is 80.
**Swimmer B: 75, 82, 81, 86, 86, 79, 71**
1. **Mode:** The most frequent number is 86 (it appears two times).
2. **Mean:** (75 + 82 + 81 + 86 + 86 + 79 + 71) / 7 = 80 (approx).
3. **Median:** When the times are arranged in order: 71, 75, 79, 81, 82, 86, 86. The median is 81.
Now, we analyze each response:
1. **Based on the mode, Swimmer B is faster.** (False: mode for Swimmer A is 80, while Swimmer B's mode is also 86)
2. **The measures of center for Swimmer A are all the same.** (True: Mean, median, and mode for Swimmer A are all 80)
3. **Based on the mean, Swimmer A is faster.** (False: Means for both are around 80)
4. **Based on the median, Swimmer B is faster.** (True: Median for Swimmer A is 80, while for B it is 81)
The true statements among these options are:
- **The measures of center for Swimmer A are all the same.**
- **Based on the median, Swimmer B is faster.**
Thus, both the second and fourth statements are true. However, if we need to choose just one option, the statement about the measures of center for Swimmer A being the same is clearer.
**Swimmer A: 77, 80, 83, 81, 80, 80, 79**
1. **Mode:** The most frequent number is 80 (it appears three times).
2. **Mean:** (77 + 80 + 83 + 81 + 80 + 80 + 79) / 7 = 80 (approx).
3. **Median:** When the times are arranged in order: 77, 79, 80, 80, 80, 81, 83. The median is the middle value, which is 80.
**Swimmer B: 75, 82, 81, 86, 86, 79, 71**
1. **Mode:** The most frequent number is 86 (it appears two times).
2. **Mean:** (75 + 82 + 81 + 86 + 86 + 79 + 71) / 7 = 80 (approx).
3. **Median:** When the times are arranged in order: 71, 75, 79, 81, 82, 86, 86. The median is 81.
Now, we analyze each response:
1. **Based on the mode, Swimmer B is faster.** (False: mode for Swimmer A is 80, while Swimmer B's mode is also 86)
2. **The measures of center for Swimmer A are all the same.** (True: Mean, median, and mode for Swimmer A are all 80)
3. **Based on the mean, Swimmer A is faster.** (False: Means for both are around 80)
4. **Based on the median, Swimmer B is faster.** (True: Median for Swimmer A is 80, while for B it is 81)
The true statements among these options are:
- **The measures of center for Swimmer A are all the same.**
- **Based on the median, Swimmer B is faster.**
Thus, both the second and fourth statements are true. However, if we need to choose just one option, the statement about the measures of center for Swimmer A being the same is clearer.
There are no human answers yet. A form for humans to post answers is coming very soon!