Which of the following is not a property of the median?

Which of the following is not a property of the median?

• A. Not affected by extreme values
• B. Uniqueness - Only 1 median exists in one set
• C. Simplicity - Very easy to calculate
• D. Affected by extreme values

Answer: (D)

The main idea here is that the median is resistant to extreme values because it is based on order, not on the actual sizes of the numbers. When you line up the data from smallest to largest, the median is the middle value (or the average of the two middle values if the sample size is even). Because it depends on position, a few very large or very small outliers don’t pull the central value toward them the way they would with the mean. A concrete example helps: for data 1, 2, 3, 1000, 1001, the median is 3, while the mean jumps to 201.4 due to the outliers. This shows that being affected by extreme values is not a property of the median. Therefore, the statement that the median is affected by extreme values is not true. The median is uniquely defined for a finite data set (for even sizes, it’s the average of the two central values), and it’s straightforward to compute by sorting and picking the middle value(s).

The main idea here is that the median is resistant to extreme values because it is based on order, not on the actual sizes of the numbers. When you line up the data from smallest to largest, the median is the middle value (or the average of the two middle values if the sample size is even). Because it depends on position, a few very large or very small outliers don’t pull the central value toward them the way they would with the mean. A concrete example helps: for data 1, 2, 3, 1000, 1001, the median is 3, while the mean jumps to 201.4 due to the outliers. This shows that being affected by extreme values is not a property of the median.

Therefore, the statement that the median is affected by extreme values is not true. The median is uniquely defined for a finite data set (for even sizes, it’s the average of the two central values), and it’s straightforward to compute by sorting and picking the middle value(s).