Median (Statistics)

The middle value of a distribution or average of the two middle items, denoted $\mu_{1/2}$ or $\tilde x$ . The Mean is approximately $\pi/2$ less than the median. The median is less efficient than the Mean for small sample sizes, but is less sensitive to outliers than the Mean (Kenney and Keeping 1962, p. 211).

For large samples with population median $\tilde x_0$ ,

$\displaystyle \mu_{\tilde x}$	$\textstyle =$	$\displaystyle \tilde x_0$
$\displaystyle {\sigma_{\tilde x}}^2$	$\textstyle =$	$\displaystyle {1\over 8N f^2(\tilde x_0)}.$

The median is an L-Estimate (Press et al. 1992).

See also Mean, Midrange, Mode

References

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 694, 1992.