Chapter 4: Analysing the Data Part II : Descriptive Statistics

# Choosing a measure of central tendency

With three seemingly sensible measures of central tendency, how do you know which one to use? Not surprisingly, the answer depends a lot on the data you have and what you are trying to communicate.

While the mean is the most frequently used measure of central tendency, it does suffer from one major drawback. Unlike other measures of central tendency, the mean can be influenced profoundly by one extreme data point (referred to as an "outlier"). For example, suppose one additional respondent answered that he (or she?) had 200 sexual partners last year (!) The inclusion of this person would increase the mean from 1.864 to 2.977. Using the mean as our definition of "average" or "typical," weÕd conclude that UNE students sleep around quite a bit more than we would conclude if this person was not included in the data.

The median and mode clearly donÕt suffer from this problem. With the "200" person included in the data, the mode would still be "1", as would the median. So the mode and median tend not to be influenced much, if any, by one or two extreme scores in the data.

There are certainly occasions where the mode or median might be appropriate, but it depends on what you are trying to communicate. Suppose, for example, that you are an employee at a company that pays its employees illegally small salaries. Suppose in this small company, there are 100 employees who make \$5000/yr, one manager who makes \$100,000/yr, and one CEO who makes \$2,000,000/yr. The owner of the company could claim that the mean salary is over \$25,000. But as an employee, you might complain to the government, and point out that the modal salary is only \$5000/yr, or that half of the employees make \$5000 or less (the median). None of these claims are wrong, and each serve a certain function for the person attempting to make a point. In this context, most would argue that the mean really isnÕt appropriate because the CEOÕs salary is shifting the mean so much. If you take out the CEOÕs salary, the mean drops considerably to almost \$6,000.