When reading technical papers, I often hear the terms "mean relative
absolute difference" and "median relative absolute difference."

I'd like to know:
-the definitions of these terms
-what they are used for
-how they are calcualted (ie: an example of how they could be calculated)

Thanks,
Kristen

Without getting into "relative absolute difference" (a Researcher will
do that) I'll say this:

Mean is average. Add everything up and divide by the number of things
you added up. (Mean of 3 + 4 + 18 + 20 + 5 is 10)

Median is the midpoint. Half are more and half are less. (The median
of 3, 4, 5, 18 and 20 is 5. Note that the median of the range from 3
to 20 is 11.5).

Kristen, 

Mean is the sum of all data points, divided by the number of data
points.  (As stated by markvmd-ga above).

Median is indeed the midpoint of all the data points when sorted in
order.  There are two cases however...

If there is an ODD number of data points (i.e. 5 data points), then
the median is the data point in the middle.  In this case 2 data
points lie to the left of the median point, and 2 data points lie on
the right of the median point.

If there is an EVEN number of data points (i.e. 6 data points), then
the median is the average of the two middle points... for instance,
say you have the data points  3,5,6,7,8,10.  Then the Median here is
(6+7)/2 = 6.5


The terminology "absolute relative difference" refers to the
difference between two measurements of the mean/median such that if
the difference is negative, the value is given as positive... and if
the difference is positive, the value is again given as positive.

So say you have group A with a mean height of 5.4 inches.  And group B
with a mean height of 5.8 inches.

What is the "absolute relative difference" of measurement A MINUS measurement B?

The answer is...

Measurement A - Measurement B = 5.4 - 5.8 = -0.4 = 0.4 (the negative
is dropped due to the "absolute" clause in the sentence.

Often, mathematical papers will formally put math that is absolute in
bars that look like this -->   |  |  (known as absolute-value bars)

i.e.  |-0.4| = 0.4

The exact same reasoning applies if the question asked for the
absolute median difference instead of the absolute mean difference.

Hope this helps.