When is the distinction between mean and a median important?

•Mean (i.e.
Arithmetic Average)

–Used when data
is approximately normally distributed

•Median

–Sometimes used
with skewed data due to its robustness

–Preferred on Likert scales (survey data) since values are ranked but their differences are not clearly
quantifiable.

•After all, what number does “agree” minus
“disagree” equal? Regardless
of how one quantifies these differences, the median remains the same, but the mean depends on the scale.