Here is the file I made on RMS. DOes this help make things more clear?
hi dknguyen, what do you mean weighted average? is it the same as average value or average mean?
Okay, forget everything you learned about "averages" or "means". The average/mean that you learned are all special cases of the weighted average. THe special case being that all items have equal weightings. Think about how your grade in a class is calculated...
If you have 5 quizzes worth 10% each, and one final worth 50%, then the REGULAR AVERAGE of your quizzes is:
How would you calculate your average mark for the quizzes (not including the final)? Obviously you just go:
(Quiz1 + Quiz2 + Quiz3 + Quiz4 + Quiz5)/5
because you have 5 items of equal weighting. But really, this is just a simplification of the weighted average equation because you have equal weightings. THis simplified expression actually comes from the more general weighted average equation:
(Quiz1*10% + Quiz2*10% + Quiz3*10% + Quiz4*10% + Quiz5*10%)/50%
which simplifies down to
(Quiz1*0.2 + Quiz2*0.2 + Quiz3*0.2 + Quiz4*0.2 + Quiz5*0.2) --->>>
(Quiz1 + Quiz2 + Quiz3 + Quiz4 + Quiz5)*0.2 --->>>
(Quiz1 + Quiz2 + Quiz3 + Quiz4 + Quiz5)/5
But now think of your final grade...it's not simply an average of your quizzes and final exam because your final exam was worth much more than the others (it was weighted more heavily). Since the items now have different weights, no regular average exists. Instead, only the more general weighted average exists:
(Quiz1*10% + Quiz2*10% + Quiz3*10% + Quiz4*10% + Quiz5*10% + Final*50%)/100%
which again simplifies down to
(Quiz1*0.1 + Quiz2*0.1 + Quiz3*0.1 + Quiz4*0.1 + Quiz5*0.1 + Final*0.5)
It seems silly that I wrote 10%, 50%, and 100% and then simplified them to 0.1, 0.5, and 1. BUt this is just because the marks are in percentages which are already a fractional form. But in an example like RMS, these numbers would end up being time segments of the waveform, and 100% would end up being the period of the waveform. So in this case, it obviously isn't so silly, since you are now finding the ratio of
"some time segment" : period
whereas before you were finding the ratio of
"some %" : 100%
which is redundant since % is already a ratio.
Understand? I am a bit curious to what level of schooling you are in right now. Because by the time you get to high school most everyone knows what a weighted average is (if only so they can calculate how well they need to do on the final exam to pass).
THIS IS THE FINAL VERSION OF THIS POST.