Weighted Average: Tutorial and Calculator (gc.mes.fm/wac) (Notes)

in mathematics •  5 months ago  (edited)

In this video I go over what a weighted average is and how it compares with the basic average calculation. I also go over our Weighted Average Calculator, at https://gc.mes.fm/wac, which although is used for calculating the weighted average course grade, it can still be used for calculating the weighted average of any set of numbers. Also, as shown in the video, I illustrate how the basic average calculation is identical to the weighted average except that the weights or worth of all the numbers are the same. This means that our weighted average calculator can also be used to calculate the basic average by simply inputting the same number for the weights of all the courses. Check out our calculator and let us know what you think as well as if you have any suggestions for making it even better!


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Weighted Average: Tutorial and Calculator (gc.mes.fm/wac)

We recently created a weighted average calculator which is used mainly for calculating your weighted average course or semester grade; but can be used for any type of weighted average.

The calculator can be found at gradecalculator.mes.fm/weighted-average-calculator or through the shortened URLs: gc.mes.fm/weighted-average-calculator and gc.mes.fm/wac.

Before I go over the calculations behind our calculator, let's us go over what a weighted average as well as what an average is:

What is an Average?

The average of a group of numbers is simply defined as the sum of the numbers divided by the total amount of the numbers. This definition yields a number that when multiplied by the amount of numbers is equal to the sum of the numbers; This number is known as the average and is illustrated in the example below:

Example:

What is a Weighted Average?

A weighted average is the same as an average except that each number is scaled by importance. This simply means that each number has an associated weight or worth and its importance is calculated by multiplying the number by its weight. The weighted average is calculated as the sum of all the numbers multiplied by their weights divided by the sum of the weights. As shown in the following example, it turns out that an average is simply a weighted average except all the numbers have the same weights. And similar to the average, this definition yields a number that when multiplied by the sum of the weights is equal to the sum of all the numbers multiplied by their weights.

Example:

If we assume that the weights in the above example were all the same, W, then the weighted average is simply the average:

This means that for calculating the average, the weight of the numbers don't matter and when using our calculator to calculate the average you can simply input the same number for the weights, as shown in the example below:

Example using our Weighted Average Calculator

The calculations used in this example are identical with the calculations in the above examples:

To get the average grade, we simply input in our calculator the same weights for each course, for example choosing the number 1:

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