Mean

Notation is X with a line over it.

The mean is the average of a group of numbers. It is the most used measures of central tendency and the most precise of inferential purposes. The mean is influenced by every number in a group and consequently is most affected by skewed distributions. The mean has very nice properties for lots of fancy statistics.

The mean of a group of scores is that point on the number line such that the sum of the squared distances of all scores to that point is smaller than the sum of the squared distances to any other point. Glass & Hopkins, p. 58

If the mean is substituted for every number in a group, the sum of the squares results in the least amount of error.

The mean is useful for interval and ratio values. The big X with the line over it is called "X Bar". The big E-looking thing is a sigma and tells you to sum something. The i=1 part says to start the summing with the first observed value. The little n over the sigma means to continue summing all the way to the last observed value. The Xi means that you are summing values of X. The whole thing is over n, again standing for the total number of observations. If there is no beginning and ending value specified, you are using all of the observations in X.

The three most common measures of central tendency are the mean, the median, and the mode.

page revision: 16, last edited: 20 Sep 2008 00:07