A data set has a median of 63, and six 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 63, what is the value of n?
A) 13
B) 10
C) 12
D) 16

Question

Quizplus · Accepted Answer

If the median is 63, then there are an equal number of numbers above and below 63 in the data set.
If six numbers are less than 63, then six numbers must be greater than 63.
Therefore, there are 12 numbers in total in the data set.
Since n is even, we know that the total number of numbers is divisible by 2.
If none of the numbers are equal to 63, then there are 11 possible numbers that can be greater than 63 and 11 possible numbers that can be less than 63.
Therefore, there are 22 possible numbers in total, which is not divisible by 2.
The only even number between 12 and 22 is 12, so n=12.

A Data Set Has a Median of 63, and Six