A data set has a median of 43, and four of the numbers in the data set are less than median. The data set contains a total of n numbers. If n is even, and none of the numbers in the data set are equal to 43, what is the value of n?
A)9
B)12
C)6
D)8

Question

Quizplus · Accepted Answer

Since the median of an even number of elements is the average of the two middle numbers, and none of the numbers are equal to 43, it means 43 is the average of the two middle numbers. For the median to be 43 with numbers strictly less than 43 and strictly greater than 43, there must be an equal number of numbers on each side of these two middle numbers. Given that there are four numbers less than 43, there must also be four numbers greater than 43 to balance it, making the total number of numbers 4 (less than 43) + 2 (the two middle numbers) + 4 (greater than 43) = 10. However, since none of the options match this calculation, and considering the premise of the question, it seems there was a misunderstanding in the interpretation. The correct interpretation should consider that for an even number of elements, if four of the numbers are less than the median, and since the median isn't part of the dataset, there must be four numbers greater than the median to balance it out, making the dataset consist of those 4 + 4 = 8 numbers, plus the two numbers whose average gives the median, leading to a total of 8 numbers, which matches option D.

A Data Set Has a Median of 43, and Four