In deriving statistics, we talk about "weight" to assign to each observation. When I learned it the first time,
it took me a while to get it, but I felt I understood it completely when I realized that even without weight, we are assigning
a weight of 1 to observations, i.e., we are saying to our statistical software or Excel, "please treat each individual
case as one case." For example, let's say we want to get an average score of three persons' test score:
What I did was 50 + 60 + 40 and divide the result by 3 (count of observation). In this calculation, you don't see
any weights used. But in fact they are there:
(50*1) + (60*1) + (40*1) and divide the result by (1+1+1, the number of weights).
Notice I now call count of observation "the number of weights."
So if for some reason if you want to treat each observation (each person) with different weights, that is possible.
For example, for a strange reason you want to count John's response twice. You assign a weight of 2 to Mr. John
(treating him as if he is worth two persons), but treat everyone else as 1 (one person).
(50*2) + (60*1) + (40*1) and divide the result by (2+1+1, the number of weights).
What about the case when you don't want to include John into calculation. John is a new student to the class, so,
say, a teacher didn't want to include his score to the average test score that he needs to report to the school district.
Then you assign 0 to John:
(50*0) + (60*1) + (40*1) and divide the result by (0+1+1, the number of weights).
From this you realize you are already doing a lot of weighting. You only considered John, Mary, and David, but
you are ignoring the rest of classmates. You are assigning 0 to all these people:
(50*1) + (60*1) + (40*1) + (35*0) + (26*0) + 25(*0) ...
and divide the result by (1+1+1+0+0+0...., the number of weights).
You are already using weights; you may not be aware of it.