Sample Mean

The sample mean of a set  of  observations from a given distribution is defined by

It is an unbiased estimator for the population mean . The notation  is therefore sometimes used, with the hat indicating that this quantity is an estimator for .

The sample mean of a list of data is implemented directly as Mean[list].

An interesting empirical relationship between the sample mean, statistical median, and mode which appears to hold for unimodal curves of moderate asymmetry is given by

(Kenney and Keeping 1962, p. 53), which is the basis for the definition of the Pearson mode skewness.

REFERENCES:

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, p. 16, 2000.

Kenney, J. F. and Keeping, E. S. "Averages," "Relation Between Mean, Median, and Mode," and "Relative Merits of Mean, Median, and Mode." §3.1 and §4.8-4.9 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 32 and 52-54, 1962.