Mean and Median

The mean is the arithmetic average of a group of numbers. Its relative ease of calculation—any spreadsheet program will compute a mean—and widely understood definition make it a common point of reference in many types of research. More important than its common use is its role in characterizing a data set. In a normally distributed data set, the mean represents the population parameter, or the typical response (found under “measures of central tendency” in statistics programs). Public relations researchers and practitioners often focus on the “average person's opinion” when investigating attitudes or planning campaigns. For example, on a five-point Likert item (1: strongly agree to 5: strongly disagree), one may report that the mean [Page 516]response was 2.2, which corresponds to agreement, but not strong agreement. The tendency to report that “68 percent of the respondents agreed or strongly agreed” with a statement should be avoided, as it lacks the overall precision of the mean and can mask a large portion who disagree with the statement.

In addition, using the mean provides a precise benchmark from which to measure progress. In research or campaign planning, measuring opinion change from time 1 to time 2, for example, is important for improving our knowledge of the impact and effectiveness of public relations activities and for the accountability of programs. As a campaign objective, with the initial measure of 2.2 one can set a precise target of, say, 1.4 for improved agreement with a statement after the communication campaign. Measurement with the same statement at both times allows direct comparison and evaluation of change.

The mean is also important as the basis for the calculation of numerous inferential statistics. T-tests and ANOVAs, which measure differences between groups, both assume an accurate mean in the computations. Very often we need to know if, for example, gender (a t-test) or education level (an ANOVA) makes a difference in what people think about a topic or how they react to a message. Questions attempting to measure such opinions or attitudes should always be formulated in a manner that provides an accurate mean. Aside from their inability to measure a range of opinions, “yes/no” questions do not allow the calculation of a mean; only response percentages can be reported from these questions (yes/no questions can be used, however, as the grouping variable in a t-test).

The median is another measure of central tendency. When all responses to an item are placed in numeric order, the median is the number that is the midpoint of the list. If the list has an even number of entries, the median is calculated by averaging the two numbers that fall to either side of the midpoint. In a normally distributed data set, the median and mean will be approximately the same. However, the median is useful as a measure of central tendency when the mean is either inflated by large responses or deflated by small ones. For example, in examining the income figures within an organization of 50 people, very high salaries among 6 executives could inflate the mean income in such a way that makes it look like the company pays its employees better than it does.

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