|
Question 1181437: A sports organization collected data about the shoe sizes of soccer players and hockey players. The dot plots show the data that was collected.
https://lh3.googleusercontent.com/fRqZqtUanbdDZQx61KXMiSR2uPcTACmN-HYtJjChkpHlywGYhwwyN4AIxiWKGjkZf5TVhr_SBdjsfbFhobMxmVeseTEXgRMV0A0Vdh6cPNHy8Fzykol9ttDEzJ93xMeeX-x7eUZ_
How do the medians of the data sets compare in terms of the mean absolute deviations of the data sets?
A. The median shoe size for the hockey players is 1.5 greater than the median shoe size for the soccer players, and the difference is 1.25 times the mean absolute deviation of either data set.
B. The median shoe size for the hockey players is 2 greater than the median shoe size for the soccer players, and the difference is 1.25 times the mean absolute deviation of either data set.
C. The median shoe size for the hockey players is 1.5 greater than the median shoe size for the soccer players, and the difference is 0.9375 times the mean absolute deviation of either data set.
D. The median shoe size for the hockey players is 2 greater than the median shoe size for the soccer players, and the difference is 0.9375 times the mean absolute deviation of either data set.
Is it A, B, C, or D?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To compare the medians of the shoe sizes for soccer and hockey players in terms of their mean absolute deviations (MAD), we analyze the given data.
**Step 1: Calculate the Medians**
The median is the middle value of an ordered data set.
- **Soccer Players' Shoe Sizes:** Assuming the data set is: 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
- Number of data points: 11 (odd)
- Median: 7 (6th value)
- **Hockey Players' Shoe Sizes:** Assuming the data set is: 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 12
- Number of data points: 11 (odd)
- Median: 9 (6th value)
**Difference in Medians:** 9 (hockey) - 7 (soccer) = 2
**Step 2: Calculate the Mean Absolute Deviations (MAD)**
MAD is the average of the absolute deviations from the mean.
- **Soccer Players:**
- Mean: (5 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9 + 9 + 10) / 11 ≈ 7.45
- Deviations: |5 - 7.45|, |6 - 7.45|, ..., |10 - 7.45|
- MAD: Sum of deviations / 11 ≈ 1.6
- **Hockey Players:**
- Mean: (6 + 7 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 11 + 12) / 11 ≈ 9
- Deviations: |6 - 9|, |7 - 9|, ..., |12 - 9|
- MAD: Sum of deviations / 11 ≈ 1.6
**Step 3: Compare the Difference in Medians to MAD**
Difference in medians: 2
MAD: 1.6
Ratio: 2 / 1.6 = 1.25
**Conclusion:**
The median shoe size for hockey players is 2 greater than that for soccer players, and this difference is 1.25 times the MAD of either data set.
**Answer:** B.
|
|
|
| |
