Streiner D L
Kunin-Lunenfeld Applied Research Unit, Baycrest Centre for Geriatric Care, 3560 Bathurst Street, Toronto, ON M6A 2E1.
Can J Psychiatry. 2000 Nov;45(9):833-6. doi: 10.1177/070674370004500908.
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.
一组数字的集中趋势有许多指标，包括众数、中位数和平均数。实际上，有好几种“平均数”，算术平均数只是其中之一。当数据呈偏态分布时，或者当分布的一端或两端存在可能扭曲结果的异常值时，平均数的“稳健”估计量，如截尾平均数或双平方加权平均数，会比算术平均数给出更好的结果。如果数据反映的是随时间的增长，几何平均数比其他指标更能准确反映中间点，并且在确定各组样本量不同时的样本量时，调和平均数是首选。最后，本文讨论了“平均数”一词在通俗用法和统计用法之间的差异，以及这种差异如何导致解释上的问题。
