How does the median differ from the mean in the presence of outliers?

The median differs from the mean significantly in situations where outliers are present, primarily due to their definitions and how they are calculated. The mean is the arithmetic average of all values in a data set, meaning that every value, including outliers, directly influences it. For example, if a data set contains one very high or very low value compared to the rest, the mean can shift significantly, thereby misrepresenting the central tendency of the data set.

In contrast, the median represents the middle value when all numbers are arranged in order. Because it is determined solely by the position of values in a sorted list and not by their magnitude, the median remains largely unaffected by extreme values or outliers. This stability makes the median a more reliable measure of central tendency in skewed distributions or sets with outliers.

Consequently, the mean being influenced while the median remains stable accurately describes the relationship between these measures in the context of outliers.