24. What is the median of the following set of data: 11, 12, 18, 14, 22, 17, 17, 12, 26, 12, 13?
Answer: B
The median of the data set is 14.
To find the median, the data must first be arranged in ascending order: 11, 12, 12, 12, 13, 14, 17, 17, 18, 22, 26. With 11 numbers in the set, the median is the middle number, which is the sixth value in this ordered list, resulting in a median of 14.
A) 12
While 12 is the most frequently occurring number in the data set, it is not the median. The median is the middle value of the ordered data set, which is 14 in this case. Thus, option A is incorrect.
B) 14
This is the correct answer as it represents the middle value of the ordered data set. When arranged, the sixth number is 14, confirming that it is indeed the median.
C) 15
Option C is incorrect because 15 is not present in the data set. The median is determined by the actual values within the set, and since 15 does not appear, it cannot be the median.
D) 15.8
This option is incorrect as it is not a value present in the data set. The median is strictly defined by the middle value of the ordered numbers, and since 15.8 is not an element of the data, it cannot be considered the median.
Conclusion
The correct answer is 14, as it accurately reflects the median of the ordered data set. All other options fail because they either misrepresent the middle value or do not belong to the set of numbers provided, underscoring the importance of correctly identifying the median in a data analysis context.