Which statement about the median is true?

Which statement about the median is true?

• A. The median is the value that splits the data into two equal halves; for odd n it's the middle value, and for even n it's the average of the two middle values.
• B. The median is the maximum value.
• C. The median is the minimum value.
• D. The median equals the mean for all distributions.

Answer: (A)

The median is defined as the middle value that splits the ordered data into two equal halves. When there is an odd number of observations, the median is the exact middle value. When there is an even number of observations, the median is the average of the two central values. This makes it different from the maximum or minimum, and it explains why the median isn’t always the same as the mean. For example, with 1, 2, 3, 4, 5 the median is 3; with 1, 2, 3, 4 the median is (2 + 3) / 2 = 2.5. So the statement captures the precise definition of the median.

The median is defined as the middle value that splits the ordered data into two equal halves. When there is an odd number of observations, the median is the exact middle value. When there is an even number of observations, the median is the average of the two central values. This makes it different from the maximum or minimum, and it explains why the median isn’t always the same as the mean. For example, with 1, 2, 3, 4, 5 the median is 3; with 1, 2, 3, 4 the median is (2 + 3) / 2 = 2.5. So the statement captures the precise definition of the median.