In this video we discuss how to find, or calculate the weighted mean, average or score of a data set, grades, or test scores in statistics. We cover the formula used and do an example for gpa (grade point average), and an individual class grade.


Transcript/notes
There are sometimes data sets where some values are more significant, or have more weight than others. For instance you may take a class where your grade is determined by 5 different things, test 1, test 2, a written report, a group project, and homework.

The instructor puts weights on these, each test will be 20% of your grade, the written report will be worth 35%, the group project will be 15% and homework will be 10%.

Your weighted mean will determine your grade in the class with the normal grading structure as you see here.

Your results on the 5 variables are, 84 on test 1, 86 on test 2, 95 on the written report, 98 on the group project and 82 on homework.

First we are going to arrange our data in a table, with column 1 being the source or variable, column 2 being the score you got, column 3 being the weight, so 20% =’s 0.2, 35% =’s 0.35 and so on, and column 4 being x times w, which I will explain in a minute.

The short formula for finding a weighted mean is x bar =’s, the sum of x times w divided by the sum of w. X bar represents the mean, x is your scores from column 2 and w is the weight from column 3.

This symbol is the capital Greek letter sigma and it mean sum of.

The long formula for this is x bar =’s, w1 times x1 plus w2 times x2 plus w3 times x3 and so on through x5 and w5 since we have 5 variables or sources. And if there were more sources or variables, this would continue on to how many ever variables there was. And the bottom of the equation is w1 plus w2 through w5, again, more sources, this continues on.

So, the short formula makes it more compact.

In our example x bar =’s, 84 times 0.2 plus 86 times 0.2 plus 95 times .35, plus 98 times 0.15 plus 82 times 0.10, which equals 90.5. And on the bottom we have .2+.2+.35+.15+.10, which equals 1.

So, 90.5 divided by 1 is 90.5, and that is your mean, so your grade is an A, and what this is process is doing is giving a numeric weight or importance, in column 3, to each of the different variables in the data set.

This method is what is used in determining grade point average. For instance lets say your grades for a semester are listed in this table, with an a being worth 4 points and going down to a d being worth 1 point. The grades column is our x and the credits column is our w, in this instance the weighted part.

Using the formula from before, x bar equals the sum of x times w divided by the sum of w, we do the math and, end up with 47 divided by 15, which equals 3.13 as the grade point average.

Timestamps
0:00 What Is A Weighted Mean?
0:06 Example Based On Categories
0:40 Arrange Data In A Table
0:54 Short Formula For Weighted Mean
1:11 Long Formula For Weighted Mean
2:15 Quick Calculation Using Short Formula
2:56 How To Calculate GPA Example

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