Basic Weighted Average Question

riph

New Member
#1
I have a simple weighted average question and I hope it’s not too basic for this forum.

Let us say I have a scaling score from 1 to 10, in increments of 1. So:

1
2
3
4
5
6
7
8
9
10

And for each of those scores I have a population of 10.

10
10
10
10
10
10
10
10
10
10

When I multiply each population with each score, and then divide the sum of that product with the sum of the populations (the weighting values), I get a weighted value of 5.5, which I believe for my purposes skews the result too high (by a value of .5). To adjust this 5.5 to 5.0, I assume I have to include a 0 value on the 1-10 scale but I’m not sure how that would then adjust the result to 5, as I would simply be multiplying a score of 0 with a population of 0. Am I thinking about this correctly (albeit in an unsophisticated way) and what can I do to adjust the score accordingly? Or should I not adjust the score—that is, is 5.5 the correct way of averaging this and my inclination or intuition is wrong?

I’ll note further that I’m actually looking at a scale from 0 to 100, the scores of which I’m given in deciled increment ranges of 5—so 0.0-5.0, 5.01-10…95.01-100.0. Each score, like 0.0-5.01, has a corresponding population value. My inclination has been to change these to a scale of 2.5, 7.5…97.5, and then calculate the weighted average accordingly but that may be quite wrong; the only other alternative I can think of would be to calculate the weighted average with a scoring system of 5, 10...100, but that seems to skew the result high, as I outlined in the example above. Any advice here would be welcome. Thank you.
 

Mean Joe

TS Contributor
#2
as I would simply be multiplying a score of 0 with a population of 0.
This is where you skip over a part. You add a 0 score, with a population of 10. So multiply 0 score x 10 population = 0 indeed, but now the sum of the populations changes, so your weighted average would change. Down to 5.0.
 

riph

New Member
#3
Hi Mean Joe,
Are you saying I should in fact add a 0 value? Wouldn't adding a population value of 10 that doesn't exist in your data corrupt it? With the actual data set I'm looking at (described in the bottom part of my post), the population numbers vary widely--how would I determine what population value to enter at a score of 0? Thank you.