13. Find the median of the following data set: 1, 4, 2, 3, 9, 7, 12, 1, 4, 2, 8, 11, 3, 2, 4
Answer: D
The median of the data set is 4.
To find the median, the data set must first be arranged in ascending order. Once sorted, the median is the middle value, which in this case is 4.
A) 3.4
This option is incorrect because, when the data set is sorted, the middle value does not yield 3.4. The median must be a number from the set itself, and since 3.4 is not present in the sorted list, it cannot be the median.
B) 5.2
This option is also incorrect. After sorting the data set, the median cannot be 5.2 as it is not one of the numbers in the data set. The median is specifically the middle value, which does not align with this option.
C) 11
This option is incorrect as well. While 11 is present in the data set, it is not the median. The median is determined by the central value of the sorted data, which is lower than 11 in this case.
D) 4
This option is correct. When the data set is sorted as 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 7, 8, 9, 11, 12, the middle value falls at 4, making it the median.
Conclusion
The correct median of the data set is definitively 4, as it is the central number when all values are arranged in order. All other options fail because they either do not correspond to the middle value of the sorted list or are not part of the data set itself.