Weighted Average Calculator

Weighted average calculator and calculation. Weighted mean calculator.

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Here we discuss list of online math calculators that help us for doing calculation easily.

Weighted Average

The Weighted average calculator helps you find the average when the values are not weighted equally.The weighted average (x) is equal to the sum of the product of the weight (wi) times the data number (xi) divided by the sum of the weights:

Example

Find the weighted average of class grades (with equal weight) 70,70,80,80,80,90:

Since the weight of all grades are equal, we can calculate these grades with simple average or we can cound how many times each grade apear and use weighted average.

2×70, 3×80, 1×90

x = (2×70+3×80+1×90) / (2+3+1) = 470 / 6 = 78.33333

what is a weighted average?

Weighted average (weighted arithmetic mean) is a concept similar to standard arithmetic mean (called simply the average), but in the weighted average not all elements are contributing equally to the final result. We can say that some values are more important than the others, so they are multiplied by a coefficient called the weight.

For example, during your studies you may encounter the situation where the grade from an exam is two times more important than the grade from a quiz - and that's exactly what we call the weighted average method. To define it in a more mathematical way, we can write the weighted average formula as:

weighted mean formula

(w₁x₁ + w₂

x₂ +........+w_nx_n) / (w₁ + w₂ +......+ w_n)

where x₁,x₂...x_n are our numbers, and w₁,w₂...w_n are our weights - the importance of the numbers in averaging.

So, having A from an exam and C from a quiz, you'd get B as a standard average, but assuming that the exam is two times more important, you should get a B+.

How to calculate a weighted average

Let's find out how to calculate a weighted average - the easiest way is to look at the simple example:

Suppose a student has two four-credit classes, a three-credit class, and a two-credit class. Assume that the grades of the courses are as follows:

A for a four-credit class,

B for the other four credit class,

A for the three credit class,

C+ for the two credit class.

Then, we need to translate the letter grades into numerical values. Most schools in the US use a so-called 4.0 GPA scale, which is a 4 point grading scale.

So from the table we know that A = 4.0, B = 3.0 and C+ = 2.3. Now that we have all the information, we can have a look at how to calculate the GPA using a weighted average method:

1. Sum the number of credits. 4 + 4 + 3 + 2 = 13, that was a really easy step.

2. Take the value assigned to the grade and multiply by the number of credits. In our case, it will be:

A * 4 credits = 4.0 * 4 = 16

B * 4 credits = 3.0 * 4 = 12

A * 3 credits = 4.0 * 3 = 12

C * 2 credits = 2.3 * 2 = 4.6

3. Add all the values. 16 + 12 + 12 + 4.6 = 44.6

4. Divide the sum by the total number of credits. So for our example it's equal to 44.6/13 = 3.43

The whole weighted average formula may be written as:

(4 * 4 + 4 * 3 + 3 * 4 + 2.3 * 2) / (4 + 4 + 3 + 2) = 3.43

Let's compare this result to an average that is not weighted. Then we don't take the credits into account, and we divide the sum of grades by its total number.

(4 + 3 + 4 + 2.3) / 4 = 3.33

Notice how the weighted average changed. Sometimes it may be a really significant difference - like a grade difference or even whether you pass or fail your course.