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Answer :
Final answer:
Its median matches the overall median (20) and, therefore, has the least spread from it. Thus the correct answer is option is c) Median: 20, More spread out above the median.
Explanation:
To determine the overall median of the data, we first need to arrange the given medians in ascending order: 17, 20, 23, 25. The median is the middle value in this ordered list, which is 20. Therefore, the overall median of the data is 20.
Now, let's assess whether the numbers in the two middle groups are more spread out above or below the median. We can see that the medians in group a and group c are both above the overall median of 20, while the medians in group b and group d are both below it. To determine which set of numbers is more spread out, we should consider the absolute differences between each median and the overall median:
For group a: |23 - 20| = 3
For group b: |17 - 20| = 3
For group c: |20 - 20| = 0
For group d: |25 - 20| = 5
The absolute difference measures how far each group's median is from the overall median. A smaller absolute difference indicates that the data points are closer to the overall median, while a larger absolute difference suggests that the data points are more spread out from the overall median.
Based on these calculations, we can conclude that groups a and b both have an absolute difference of 3, but group d has a larger absolute difference of 5. Therefore, the numbers in the two middle groups, a and b, are more spread out above the median (20) than below it.
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