Answer :
To solve this problem, we're looking to find the ratio of the difference in the means of the two teams to the mean absolute deviation (MAD) of Team B. Here's how you can do this step-by-step:
1. Understand the Problem:
- You are given the means of two teams, let's call them Team A and Team B.
- Additionally, you have the mean absolute deviation of individual times for Team B.
2. Identify the Given Values:
- Mean for Team A (`mean_A`) = 59.32 seconds.
- Mean for Team B (`mean_B`) = 59.1 seconds.
- Mean Absolute Deviation of Team B (`mad_B`) = 59.1 seconds.
3. Calculate the Difference in Means:
- Subtract the mean of Team B from the mean of Team A:
[tex]\[
\text{Difference in Means} = \text{mean}_A - \text{mean}_B = 59.32 - 59.1 = 0.22 \text{ seconds}
\][/tex]
4. Calculate the Ratio:
- Divide the difference in the means by the mean absolute deviation of Team B:
[tex]\[
\text{Ratio} = \frac{\text{Difference in Means}}{\text{MAD of Team B}} = \frac{0.22}{59.1}
\][/tex]
5. Determine the Closest Answer Choice:
- By calculating the above division, you'll find that the result is approximately 0.0037.
- Comparing this to the given options:
- 0.09
- 0.15
- 0.25
- 0.65
- The numerical result approximately 0.0037 doesn't closely match any of the provided answer choices.
Based on this calculation and the result, it seems there may be a misunderstanding or potential issue with the provided options, as none directly approximate the calculated ratio. If applicable, double-check the question or provided data for possible discrepancies.
1. Understand the Problem:
- You are given the means of two teams, let's call them Team A and Team B.
- Additionally, you have the mean absolute deviation of individual times for Team B.
2. Identify the Given Values:
- Mean for Team A (`mean_A`) = 59.32 seconds.
- Mean for Team B (`mean_B`) = 59.1 seconds.
- Mean Absolute Deviation of Team B (`mad_B`) = 59.1 seconds.
3. Calculate the Difference in Means:
- Subtract the mean of Team B from the mean of Team A:
[tex]\[
\text{Difference in Means} = \text{mean}_A - \text{mean}_B = 59.32 - 59.1 = 0.22 \text{ seconds}
\][/tex]
4. Calculate the Ratio:
- Divide the difference in the means by the mean absolute deviation of Team B:
[tex]\[
\text{Ratio} = \frac{\text{Difference in Means}}{\text{MAD of Team B}} = \frac{0.22}{59.1}
\][/tex]
5. Determine the Closest Answer Choice:
- By calculating the above division, you'll find that the result is approximately 0.0037.
- Comparing this to the given options:
- 0.09
- 0.15
- 0.25
- 0.65
- The numerical result approximately 0.0037 doesn't closely match any of the provided answer choices.
Based on this calculation and the result, it seems there may be a misunderstanding or potential issue with the provided options, as none directly approximate the calculated ratio. If applicable, double-check the question or provided data for possible discrepancies.
