Which statement correctly defines the median when a data set has an even number of values?

Which statement correctly defines the median when a data set has an even number of values?

• A. The mean of all values
• B. The mode
• C. The average of the two middle values
• D. The maximum value

Answer: (C)

When data are arranged from smallest to largest and there is an even number of values, there isn’t a single middle value. The median is defined as the average of the two central values in that ordered list. This captures the center of the data without being pulled as strongly as the mean by extreme values, and it’s different from the mode (the most frequent value) and the maximum (the largest value). For example, with values 2, 4, 7, 9, the two middle numbers are 4 and 7, and their average is 5.5, so the median is 5.5.

When data are arranged from smallest to largest and there is an even number of values, there isn’t a single middle value. The median is defined as the average of the two central values in that ordered list. This captures the center of the data without being pulled as strongly as the mean by extreme values, and it’s different from the mode (the most frequent value) and the maximum (the largest value).

For example, with values 2, 4, 7, 9, the two middle numbers are 4 and 7, and their average is 5.5, so the median is 5.5.