The purpose of measures of central tendency is to describe the variability within a data set. Is this true or false? Why?
The central measure says nothing about how the data is grouped around it.
In test scores the central measure (mean or median) is 50.
This could mean that everyone has a score between 45 and 55, OR it could mean that the scores are all over the page, and just happen to give a mean (or median) of 50.
(45-50-55 and 1-50-99 both give a mean and median of 50).