Do you see what I mean? Indices of central tendency

Abstract

There are many indices of the middle, or central tendency, of a set of numbers, including the mode, median, and mean. Indeed, there are, several "means," of which the arithmetic mean is only one. When data are skewed, or when there are outliers at one or both ends of the distribution that may distort the results, "robust" estimators of the mean, such as the trimmed mean or the bisquare weight mean, give better results than does the arithmetic mean. If the data reflect growth over time, the geometric mean is a more accurate reflection of the middle point than are other indices, and in determining sample size when the sample size varies among groups, the harmonic mean is the one of choice. Finally, this paper discusses the difference between the lay and statistical use of the term "average" and how this difference can lead to problems in interpretation.