# Why I do not need weighted average if the sum of weights equals 1?

I am a bit confused here: I have 10 tasks, each of which has a scale associated (importance) and a final score. The sum of scales is 100%. To get the overall score, I would expect to calculate a weighted average as individual tasks have different weights. But apparently, it is enough to simply multiply the scores by their weights and sum it up.

Why is that? What would have to be different so that I must use weighted average?

Because dividing by $1$ doesn't do anything, so you might as well not do it. If the weights didn't add to $1$, you would have to divide by their sum, but in this special case you don't have to. If you really want to, you can, of course.

• Well sure, that is clear, to me it sounds strange that even though some items have 50% and some only 10% of importance, in the end it does not matter for the calculation – John V Feb 4 '17 at 9:48
• No, they're still multiplied by their weights. So one is multiplied by $0.5$ and the other by $0.1$. – Arthur Feb 4 '17 at 10:03