Even-number data set: If a data set has two middle numbers, how is the median defined?

Even-number data set: If a data set has two middle numbers, how is the median defined?

• A. The smaller of the two middle numbers
• B. The average of the two middle numbers
• C. The larger of the two middle numbers
• D. The sum of all numbers divided by count

Answer: (B)

When there are an even number of observations, there isn’t a single middle value after ordering the data. The median is defined as the average of the two central numbers. This gives a central point that splits the data into two equal halves, so about half the data are at or below it and about half are at or above it. For example, with 2, 4, 6, 8, the two middle numbers are 4 and 6, and the median is (4 + 6)/2 = 5. Using just the smaller or the larger middle value would bias toward one end, and the mean (sum of all numbers divided by the count) is a different measure of center.

When there are an even number of observations, there isn’t a single middle value after ordering the data. The median is defined as the average of the two central numbers. This gives a central point that splits the data into two equal halves, so about half the data are at or below it and about half are at or above it. For example, with 2, 4, 6, 8, the two middle numbers are 4 and 6, and the median is (4 + 6)/2 = 5. Using just the smaller or the larger middle value would bias toward one end, and the mean (sum of all numbers divided by the count) is a different measure of center.