Measures of Variability

Value of Measures of Variability

Although researchers often place focus on measures of central tendency, such as mean, median, and mode, measures of central tendency provide an incomplete picture of a data set. Measures of central tendency provide information useful to understand the average score within the data, but the information provided is limited. Through measures of central tendency, indicators of how condensed or spread scores are within the data are unavailable. To gain a more thorough understanding of data, it is important to understand if the scores are mostly near the mean or if they are widely spread from the mean. For example, two sets of data may have the same mean, median, and mode, but the scores might be drastically different in how they are dispersed. A larger spread of data will produce a wider normal curve, and a narrower spread of data will produce a thinner normal curve. In Figure 1, both lines represent a data set with a mean of 60 and a normal distribution. The red line has a much wider variety in scores than the blue line, even though they have the same mean.

Consider the following example of an instructor analyzing exam scores in two sections of the same course. Two public speaking classes took the same exam and both show a C average in exam scores. At first glance, a C average in both classes may seem an expected result from the instructor’s perspective. Upon closer inspection the instructor notices a difference in the distribution of exam scores in the two classes (Table 1). Class B’s scores are close to the mean score, scoring at or near a C. Class B’s scores are fairly homogeneous, or similar. Class A’s scores, on the contrary, are farther from the mean, and are instead at either extreme, scoring either extremely high or low. Class A’s scores are heterogeneous, or different from one another. Both of these classes have the same average exam score, but the students in these courses performed differently on the exam. The dispersion of scores provides additional information for the instructor analyzing the scores. It seems as though students in Class B, in general, had a basic understanding of the topic. Students in Class A either understood the material extremely well or had extreme difficulty with the content of the course. This information would have been missed by only analyzing the central tendency of scores.

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