The median is a better choice than the mean for a measure of central tendency if the data:

The median is a robust estimator of location whose value is unaffected by the magnitude of extreme observations; it has a 50 % breakdown point, whereas the mean’s breakdown point is 0 %. Therefore, when a data set is prone to outliers, the median provides a truer indication of the “typical” value than the mean, which can be pulled arbitrarily far by a single extreme value. For distributions without substantial contamination, either statistic is acceptable, but under frequent or severe outliers the median is clearly preferred.

A. Bimodal data have two peaks; neither mean nor median represents either mode well—median is not conspicuously superior.
C. In a normal distribution the mean is unbiased and efficient; mean = median, so median offers no advantage.
D. Exponential distributions are skewed but rarely contain extreme contamination; both statistics are sensitive to skew, but outlier-robustness (the issue asked) is not the primary concern.

1. Wilcox

R.R. “Introduction to Robust Estimation and Hypothesis Testing

” 3rd ed.

Academic Press

2012

pp. 4-5 (median’s robustness and breakdown point).

2. Huber

P.J. & Ronchetti

E. “Robust Statistics

” 2nd ed.

Wiley

2009

Sect. 2.1

pp. 8-10 (median vs. mean under outliers).

3. MIT OpenCourseWare

6.041/6.431 “Statistics for Applications

” Lecture 1 notes

slides 16-18 (discussion of mean’s sensitivity to outliers

median’s resistance).

4. Casella

G. & Berger

R.L. “Statistical Inference

” 2nd ed.

Cengage

2002

Example 1.5 (effect of a single extreme observation on mean vs. median).

5. University of Wisconsin-Madison

STAT 471 Course Pack

Chap. 1

pp. 12-13 (choice of median for outlier-prone data).