35. The weights in pounds of 14 cats are: 8.8, 10.2, 9.6, 9.1, 10.2, 13.3, 12.6, 8.2, 12.5, 10.4, 11.7, 10.5, 10.9, 10.2. What is the median weight of the cats?
Answer: D
The median weight of the cats is 10.3 pounds.
To determine the median weight of the cats, the weights must be arranged in ascending order. When the values are sorted, the median is found to be 10.3, as it is the average of the seventh and eighth values in the ordered list.
A) 10.5
This option is incorrect because, when the weights are sorted, 10.5 does not represent the middle value. Instead, it lies above the true median, which is calculated from the two middle numbers in the ordered list.
B) 10.6
10.6 is not a viable median as it exceeds the highest values encountered in the dataset. The median should reflect a value that is present in the actual set of weights, making this answer invalid.
C) 10.2
While 10.2 is one of the weights recorded, it is not the median. The median is specifically the middle value of a sorted dataset, and in this case, 10.2 is lower than the actual median of 10.3.
D) 10.3
This is the correct answer as it is the median weight of the cats. After sorting the weights, the 7th and 8th values are both 10.2 and 10.4, respectively, and their average is precisely 10.3.
Conclusion
The median weight of 10.3 accurately represents the central tendency of the dataset after sorting. All other options are either above or below this median value, confirming that they do not align with the correct calculation based on the provided weights. Thus, 10.3 is definitively the correct answer.