Why would a human resources department use both mean and median when doing a salary evaluation of a department?

The mean is sensitive to extreme values (outliers), while the median is resistant to them. When a dataset contains outliers, such as a few very high or very low salaries, the mean will be pulled in the direction of those outliers. The median, being the middle value, will be less affected. Therefore, a large difference between the mean and median salary is a strong indicator of a skewed distribution caused by outliers. This signals to the HR department that they need to assess these extreme values to understand the true salary landscape.

A. A large difference could be due to a few very high salaries, not necessarily a need for raises for the majority of employees.

B. A difference between the mean and median is a natural property of skewed data and does not, by itself, indicate a calculation error.

D. While outliers affect the standard deviation, the direct comparison of mean and median is the classic method for identifying skewness caused by these outliers.

1. University of California, Berkeley. (n.d.). Data 8: The Foundations of Data Science. Chapter 14.1: "Properties of the Mean." Retrieved from https://inferentialthinking.com/chapters/14/1/PropertiesoftheMean.html (This chapter explains how the mean is sensitive to outliers, unlike the median, and how their difference indicates skew).

2. Tufts University OpenCourseWare. (n.d.). BIO 132: Biostatistics. "Summarizing Data." (This course material describes how comparing the mean and median is a way to assess the symmetry of a distribution and detect the influence of outliers).