Clear example of pros and cons depending on which side of the table you are on taken from a math forum.
why do we use mean instead of median
Hi Jill,
Probably the easiest way to see the difference is to consider some
data with an outlier. For example, suppose there are 7 people who
graduate from some university with degrees in communications. They all
get jobs, and their salaries are
$27,000
$29,000
$33,000
$34,000
$35,000
$39,000
$5,000,000
The last guy got a job playing basketball in the NBA! Now, the median
is the middle value, or $34,000. But the mean is about $750,000.
The $5 million salary is what we call an "outlier". :^D
So, if you were trying to tell prospective communications majors what
they could expect to earn after graduation, which number would give
them a more accurate picture--the median, or the mean?
On the other hand, if you were just trying to get people to come to
your university, which number would attract more students?
This is why it's important to understand when someone reports an
"average" value, he might be talking about the mean, the median, or
the mode (another "middle" value), depending on what kind of
impression he wants to make. It's up to _you_ to ask, in each case,
_which_ average he's talking about.
http://mathforum.org/library/drmath/view/65606.html