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April 1, 1999


Median is not mathematical mid-range

To the editor:

I am writing about an inaccuracy in the article on "average" salaries which appeared in the March 18, 1999, issue of the University Times. The article summarizes salary data from a report by Pitt's Office of Institutional Research in accordance with Pennsylvania's Financial Disclosure Law.

According to the article, "the report reveals mean (average) and median (mid-range) salaries for…each Pitt responsibility unit as of October 31, 1998." The article then lists the various means and mid-range values.

I wish to point out that "median" and "mid-range" are different statistical measures, determined by different formulas, and more importantly, can give very different pictures of the same data.

The median is typically used to present a picture of the "middle" that is uninfluenced by an extremely high or extremely low data value(s). As many data values will be above the median as below it. It thus provides contrast to the mean, which can be greatly influenced by extreme values. It is for this reason that selling prices of houses in a given community, for example, are typically reported with the median and not the mean.

The mid-range is found by simply adding the smallest and largest values and dividing by 2. The mid-range, like the mean, can be greatly affected by an extremely high or extremely low value.

There is another important distinction between the median and mid-range. A desirable property of any statistic is that it be based upon as much information as possible. Therefore, ideally it should be calculated using all the data values, as are the mean and median. The mid-range fails in this respect, as it is calculated using only two data values, ignoring all the rest.

I will also add, for those who are not familiar with statistical terms, that the mid-range is a relatively obscure statistic. It is not even mentioned in most statistics textbooks.

In sum, the most logical statistic to use in summarizing salary information is the median.

To instead use other measures is to invite the mistrust and skepticism with which statistics is unfortunately all too often linked in the public's perception.

Walter J. Orange

Assistant Professor

Mathematics and Statistics

Greensburg Campus

Editor's note: The University Times used the term "mid-range" (misleadingly, as Professor Orange points out) in an attempt to indicate the point at which there are an equal number of salaries above and below that value.

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