/sci/ - Science & Math » Thread #13792175

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Weighted Average

Anonymous Tue 26 Oct 17:08:54 2021 No.13792175 View Reply Original Report

Quoted By: >>13792234

Math experts, please help:

Is it possible to find the varying degrees of importance of the numbers in a data set, regarding the weighted average?

If I am not making myself clear, sorry. But here's the scenario:

On that picture there are the results of five physical exercises. The final grade is not a normal average, but a weighted average.

I do not know the scale (what value corresponds to the maximum grade), nor how much is each exercise worth.

Is there a way to find it, having only this data?

Anonymous

Anonymous Tue 26 Oct 2021 17:09:50 No.13792178 Report

Quoted By:

Each line has the scores of a different athlete.

Anonymous

Anonymous Tue 26 Oct 2021 17:22:20 No.13792204 Report

Quoted By: >>13792211

This is a system of linear equations.
>13.96a + 4b + 6c + 2d + (1-a-b-c-d)13 = 11
>15.24a + 3b + 8c + 2d + (1-a-b-c-d)12 = 10
>14.66a + 4b + 8c + 2d + (1-a-b-c-d)17 = 11
>12.18a + 5b + 11c + 3d + (1-a-b-c-d)35 = 13
>12.20a + 7b + 11c + 3d + (1-a-b-c-d)41 = 14
There's 4 unknowns and 5 equations. That's all you need for a unique solution. There are many ways to solve a system of linear equations so just pick the one you're most comfortable with.

Anonymous

Anonymous Tue 26 Oct 2021 17:23:36 No.13792211 Report

Quoted By:

>>13792204
Just in case you need a refresher:
https://en.wikipedia.org/wiki/System_of_linear_equations

Anonymous

Anonymous Tue 26 Oct 2021 17:30:11 No.13792234 Report

Quoted By: >>13792367

>>13792175
This is a system of linear equations
>13.96a + 4b + 6c + 2d + 13(1-a-b-c-d) = 11
>15.24a + 3b + 8c + 2d + 12(1-a-b-c-d) = 10
>14.66a + 4b + 8c + 2d + 17(1-a-b-c-d) = 11
>12.18a + 5b + 11c + 3d + 35(1-a-b-c-d) = 13
>12.20a + 7b + 11c + 3d + 41(1-a-b-c-d) = 14
There are 4 unknowns and 5 equations so that's all you need for a unique solution. Just pick your favorite method: https://en.wikipedia.org/wiki/System_of_linear_equations#Solving_a_linear_system

Anonymous

Anonymous Tue 26 Oct 2021 18:22:41 No.13792367 Report

Quoted By: >>13793967

>>13792234
That sounds amazing.But I am terrible at math, hence asking for help here. How exactly do I calculate it? I am having trouble following the instructions on that Wikipedia page...

Anonymous

Anonymous Wed 27 Oct 2021 03:55:26 No.13793921 Report

Quoted By:

using the log value for differences to the mean can give a somewhat standard value to make each activity comparable.

Anonymous

Anonymous Wed 27 Oct 2021 04:17:55 No.13793967 Report

Quoted By: >>13793989

>>13792367
A+b =3
A-b=1
Assuming these two equations are regarding the same subject we can use them with one another to find definite solutions to A and b
A+A =2A, b+(-b) =0 , 3+1 = 4. 2A =4 , A=2 -> b=1
You problem can be solved in a similar way except that it has more variables but with enough equations you can determine definite solutions for the various weights
Look up matrix's and reduced rho echelon form

Anonymous

Anonymous Wed 27 Oct 2021 04:27:54 No.13793989 Report

Quoted By:

>>13793967
isnt the point to allow the comparability of these "peoples" performances and rank them? like if you were doing fantasy baseball and wanted to rank hitters across hits, runs, RBI, homers, and steals. it seems like you are answering a different question

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