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.
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.
of 
observations from a given distribution
is defined by
.
The notation 
is therefore sometimes used, with the hat indicating that
this quantity is an estimator for 
.
