Common Measures of Central Tendency: Mean, Median, Mode and JAN’s Cost of Accommodation
Posted by JAN Tech on October 15, 2009 under Accommodations | 
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From JAN E-news Volume 7, Issue 4, Third Quarter 2009
Recently, JAN’s Workplace Accommodations: Low Cost, High Impact Fact Sheet, which provides new research findings addressing the costs and benefits of job accommodations for people with disabilities, was updated. These data indicated that the “typical” one-time cost of accommodation reported by employers was $600 (JAN, 2009). Because too few employers provided cost data on accommodations that are recurring, the results focused on those with one-time costs. What does this mean?
Let’s start by deciphering the term “typical” cost. All data sets have constructs that best represent the distribution of the data. When we have several elements of a data set, we want to find one measure of central tendency, if possible, that best represents these data. This gives us a clearer picture of what is happening and allows us to make inferences about the data. For some data sets either the mode, mean, or median may be the best choice. For others, all two or three may be reported to provide readers with additional information.
The mode, the most frequently occurring number in a data set, is often used with non-numerical data. Because of this, JAN rarely reports the mode as a measure of the one-time cost of accommodation reported by employers. If using the mode as the typical cost indicator in the most recent update, the typical one-time cost of accommodation, when including those that cost nothing, was $0. When using the mode as the typical cost indicator and excluding those that cost nothing, the typical cost of accommodation was $100. Using the mode as a representative measure of central tendency for these data is probably not a good representation of what employers report as the cost of accommodation.
The mean usually refers to the arithmetic mean, which is the average of a data set. Because the mean is primarily used for symmetrical distributions with no outliers, JAN rarely reports the mean cost of accommodation reported by employers. For example, say one employer reported to JAN that it modified a building to add an elevator and reported this cost of accommodation as $100,000. Reporting an average as the cost of accommodation, when most accommodations cost far less, would not represent the typical cost of accommodation. Because most accommodations are low cost, any high dollar outliers would pull the average cost of accommodation away from the typical cost of accommodation. If using the mean as the typical cost indicator in the most recent update, the typical one-time cost of accommodation, when including those that cost nothing, was $1,183. When using the mean as the typical cost indicator and excluding those that cost nothing, the typical cost of accommodation was $2,900. Although useful in some situations, using the mean as a representative measure of central tendency for these data is probably not the best representation of what employers report as the cost of accommodation.
The median, the middle number in a data set, is used when outliers exist in a data set. Because of outliers reported by a few employers, JAN reports the median one-time cost of accommodation as the typical cost of accommodation. If using the median as the typical cost indicator in the most recent update, the typical one-time cost of accommodation, when including those that cost nothing, was $0. JAN, however, excluded the 56% that cost nothing and reported the median of those accommodations that had a reported cost. This cost of accommodation was $600. Because of a few reported outliers, the median is a good representation of what employers report as the cost of accommodation.
Given that these three measures of central tendency have different meanings, researchers may certainly have reasons to choose one over the other when reporting JAN’s data on the cost of accommodation. Want to debate the best way to report the cost of accommodation? Post to JAN’s Blog and enjoy a community space to discuss the issue. Start blogging!
Job Accommodation Network. (2009). Workplace Accommodations: Low Cost, High Impact. Retrieved October 1, 2009, from http://www.jan.wvu.edu/media/LowCostHighImpact.doc
- Beth Loy, Ph.D., Principal Consultant