How well do you understand weighted averages?

This is something that should be taught in public school. For one thing, a student’s grade is often a weighted average of quizzes, homework, final and class participation.

Here is a non-standard application. There is a Wordle game site that I like, that, after you finish a puzzle, they give the average number of guesses among players for the word. Suppose that the average number of guesses for a word is 4.4. If we make the simplifying assumption that everyone got it in 4 or 5 guesses, what percentage of the players got it in 4 guesses?

Observing members: 0 Composing members: 0

Since I work with VWAP (volume weighted average price) everyday. I am familiar with the calculation.

However, your question is not about weighted averages, but rather about averages in general. If everyone solved the puzzle in 4 or 5 guesses and the average was 4.4, then 60% guessed 4, and 40% guessed 5.

zenvelo (39284)

That is the correct answer. It can be viewed as a weighted average. 4.4 = 0.6×4 + 0.4*5. The case of two values is easy to figure. 4.4 is 40% of the way between 4 and 5, which means that a score of 4 represents 1 – .4 = .6 or 60% of the players.

Was this not taught in elementary school? I can’t remember ever not knowing this.

I don’t know what weighted averages is, but that sounds like a very basic percentage question which people learn in school.

smudges (10413)

Say you are taking a course with a mid-term, final and three projects. The final is worth 40% the mid-term is worth 30% and the projects are all worth 10%.

Projects: 86, 92, 78
Mid-term: 90
Final: 81

86*.1=8.6
92*.1=9.2
78*.1=7.8
90*.3=27
81*.4=32.4

That is exactly how a weighted average works, The values of .4, .3 and .1 are the weights, and the requirement is that the weights add to 1.0, which is indeed the case.

While I understand the concept, I get the same answer when I add the numbers together and divide by 5. Maybe there’s a difference in the end result if there are more significant differences in the weighted numbers. ¯\(ツ)

smudges (10413)

@smudges consider these scores:
Weight Score weighted score
quiz 5% 100 5
quiz 5% 100 5
project 10% 95 9.5
midterm 30% 85 25.5
final 50% 70 35
average 90 80

This demonstrates how doing well throughout the course until the final would lower a student’s grade to a “B-/C+” level,

zenvelo (39284)

^^ Yes, makes sense.

smudges (10413)