Quantitative Methods Used in Salary Administration

Medians

One problem with using the mean salary in surveys to make compensation decisions is that the number reported may be high or low due to a skewed salary distribution. Put another way, a distribution of salaries is often skewed, with many observations at the low end and very few observations at the high end. Computing an average of such a distribution will give you an answer that is higher or lower than what you would expect to draw from that distribution. Therefore, the median is sometimes the preferred measure.

In contrast, with the mean, the median is insensitive to outliers that might be present in a distribution that may skew the calculated average.

When a sample or a population consists of an even number of observations, the median is the arithmetic mean of the two middle-most observations.

More information on the median can be found on this website: http://davidmlane.com/hyperstat/A27533.html.

Example of medians

A salary survey reports the following for the Advertising Clerk position in San Francisco, California and Brookfield, Wisconsin:

What is the median salary for the Advertising Clerk position in San Francisco and in Brookfield?

Median solution. First, rearrange the salaries in increasing order:

Then find the midpoint from the two distributions:

• The midpoint salary for the Advertising Clerk position in San Francisco, California is $55,927.
• The midpoint salary for the Advertising Clerk position in Brookfield, Wisconsin is $46,928.

Median vs. Mean

Had we used the arithmetic mean method to find the average salary for the Advertising Clerk position, we would have obtained the following:

The arithmetic mean for the position in San Francisco is:

The arithmetic mean for the position in Brookfield is:

Notice that the arithmetic mean for the Advertising Clerk position in San Francisco is higher than the median. This is due to the $87,197 observation, which may be an outlier and skews the distribution. For more information on outliers, see DLC Course 49: Regression Analysis Used in Compensation Administration.