Suppose we have a sample of exam scores from a group of
students. The scores the students earned are;
8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10
From the sample we see there are only three different scores;
8, 9 and 10. How would we calcualte the average of the exam
scores? Would we;
Add the three values together 8 + 9 + 10 and then
divide by 3? (8 + 9 + 10)/3 = 9
So the average is 9.
I think we would all agree that this is not the way to
calculate the average of these numbers.
To determine the weighted average we need to know the percent
abundance of each score. In the sample there are 16 scores, five
are 8's, nine are 9's and two are 10's. So the percent of 8's is
calculated by dividing the number of 8's by the total number and
multiplying by 100, the percentage abundance of 9's and 10's are
calcualted the same way.
To calculate the weighted average we now use the mathematical
equation;
weighted average = (score value fractional abundance)1
+ (score value fractional abundance)2 + (score
value fractional abundance)3
You might ask why don't we do the calculation the following
way;
You see we get the same answer! We can not use this later
method because we do not know the number of each isotope in the
sample, we only know the percent abundance. So we have to use the
weight average approach.
