Читать книгу Elementary Regression Modeling - Roger A. Wojtkiewicz - Страница 26

The mean is the sum of the values on an interval variable divided by the number of values. By dividing the sum by the number of units of analysis, the mean produces a number that expresses the amount of the variable per unit of analysis:

where

  is the sample mean

 ∑X is the sum of all Xs in the sample

 N is the number of units in the sample

The mean is a redistributive statistic. The mean can be viewed as adding all the X values up and then giving the same amount of X to each sample unit.

The mean combines two statistics: A sum is divided by a frequency. We typically do not use only the sum to describe a sample because the sum can be influenced by the size of the sample. The mean takes sample size into account by dividing the sum by N, the frequency of units in the sample.

A statistic that can be used with interval and ordinal variables is the median. The median is a value that divides a sample into two equal parts in terms of frequency. The median provides information about the sample that is easy to understand, perhaps more so than the mean. However, the mean is used in advanced statistics because it is amenable to mathematical manipulation and the mean is the minimum variance measure of central tendency. The median, on the other hand, does not have these properties.