32. Which of the following is the median of the data set below? 12, 19, 7, 14, 22, 26, 15
Answer: B
15 is the median of the data set.
To find the median, the data set must first be arranged in ascending order: 7, 12, 14, 15, 19, 22, 26. With seven numbers in total, the median is the fourth number, which is 15.
A) 14
Option A is incorrect because, although 14 is present in the data set, it is not the middle value when the numbers are arranged in order. The median is specifically the value that separates the higher half from the lower half of the data.
B) 15
Option B is correct as it represents the median of the arranged data set. Since there are seven values, the median corresponds to the fourth value, which is indeed 15.
C) 16
Option C is incorrect because 16 is not present in the data set at all. The median must be one of the values in the data set, and since 16 is not included, it cannot be the median.
D) 19
Option D is incorrect as it is the fifth number in the sorted data set. While 19 is greater than half of the values, it does not represent the middle value; thus, it cannot be the median.
Conclusion
The correct median of the data set is 15, as it accurately divides the data into two equal halves. All other options either misidentify the median or do not represent a value from the data set itself, confirming that 15 is the definitive median.