weighted arithmetic mean

[numtan5839]

weighted arithmetic mean will be used to calculate when each data is not important equal.
We will often see that is the calculation of GPA. so, GPA calculation we need to use a weighted arithmetic mean method.
forasmuch each subject that we study is of equal importance. Or to make it easier to understand, each subject has different credits.
so, if we use arithmetic mean method. the result will be tilted to the subjects with many credits.

The formula used for weighted averages
the sum of (the value x the weights) / sum of the weighted values

Sum.png (5.96 KiB) Viewed 223 times

For Example

Subject A: Grade 3 (3 credits)
Subject ฺB: Grade 4 (1 credits)
Subject C: Grade 4 (2 credits)
Subject D: Grade 3 (3 credits)

If we use an arithmetic mean method.
Data sum is (3+4+4+3) = 14
The result is 14 / 4 = 3.50

But, if we use a weighted arithmetic mean method.
Data sum is (3x3 + 4x1 + 4x2 + 3x3) = 30
Sum of the weighted values is (3+1+2+3) = 9
The result is 30 / 9 = 3.33
So, the GPA for this term is 3.33

References
https://www.mathpaper.net/index.php/en/5/755-arithmatics-mean
https://greedisgoods.com/weighted-average-%e0%b8%84%e0%b8%b7%e0%b8%ad/
http://119.46.166.126/self_all/selfaccess12/m6/712/math_lesson1/math6/lesson1_2/lesson1_2_3.php
https://nutnuntasen.wordpress.com/ค่าเฉลี่ยเลขคณิตถ่วงน้/
https://www.gotoknow.org/posts/266711