An outlier in a data set can significantly affect the value of the mean but not the median because the mean is calculated by adding up all the values and dividing by the total number of values, while the median is the middle value of a set of data when it is arranged in numerical order. Outliers can greatly influence the mean because they can greatly increase or decrease the sum of all the values, which changes the average. However, outliers do not significantly affect the median because the median only depends on the middle value of the data set, and not the total sum of all the values.