Measures of Central Tendency

Foundations of Central Tendency

People use the concepts of central tendency nearly every day when they compare themselves to what is perceived to be “normal” or typical. We make judgments about our physical characteristics, social status, wealth, and many others based on a perceived middle or average. Knowing the center of a particular group of people, objects, or numbers can provide valuable information about the group as a whole and allow for comparisons with other groups. These common intuitive behaviors provide foundation for the mathematical properties of measures of central tendency. Although the mathematical roots for measuring central tendency extend as far back as ancient Greece, the statistical tenets of such measurements were not solidly articulated until the 19th century. Sir Francis Galton (1822–1911) was a pioneer of using the midpoint as a way to summarize information, and he is attributed with sparking interest in using measures of central tendency and distribution to understand data. By investigating the properties of distribution, Galton was able to promote the concept of normal distribution. The idea of normal distribution is that in most circumstances as scores are added to a data set it is likely that the majority of the values will gather around the central value, with more scores closer to the center and increasingly less scores further away from the center. Seeing how data are dispersed in any given sample can help researchers better understand what the data are expressing.

Researchers can understand more about the distribution of data when there is a reference point for the center of the distribution. Knowing the center for the distribution of data provides researchers with an important reference point by which to compare data points to the center and to one another. For example, the amount data vary in any given situation is a matter of how close or distant a particular value is away from the value of central tendency. Although many naturally occurring patterns tend to follow a normal distribution (i.e., mostly symmetrical on both sides of [Page 952]the central tendency), it is important to note that distributions of data can be skewed one direction or another and more pointy or more flat (the statistical term for pointiness is kurtosis). Using frequency distributions or histograms (charts showing frequencies of data) in conjunction with measures of central tendency provides researchers with valuable information about the data sample.

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