# Weighted mean

The weighted mean is used a lot by teachers. It is also called weighted average.You will learn how to calculate the weighted average using a real life example

Since the final exam usually carries more weight, this encourages students to work hard to improve their grade on the final exam

Even if students got some bad grades in the beginning, they may still pass the class with a good grade if they ace the final exam.

This happened to me a lot and teachers love to see and reward growth

Here is how a teacher may decide to grade his class. 10% for homework assignments, 15% for quizzes, 25% for a midterm, and 50% for the final exam

Notice that 10% + 15% + 25% + 50% = 100%

Suppose the maximum score is 100 and a student gets the following scores throughtout the year:

Homework assignments: 40, 50, 60, 50, 40, 30

Quizzes: 50, 60, 20, 50, 40, 80, 30, 70

Midterm: 65

Final exam: 95

What is the weighted mean?

First, find the average score for homework assignments

40 + 50 + 60 + 50 + 40 + 30 / 6

270 / 6
= 45

Then, find the average score for the quizzes

50 + 60 + 20 + 50 + 40 + 80 + 30 + 70 / 8

400 / 8
= 50

Now you can calculate the weighted mean

weighted average = 10% × 45 + 15% × 50 + 25% × 65 + 50% × 95

weighted average = 0.10 × 45 + 0.15 × 50 + 0.25 × 65 + 0.50 × 95

weighted average = 4.5 + 7.5 + 16.25 + 47.5

weighted average = 75.75

As you can see, despite having lots of bad grades on homework assignments and quizzes and failing the midterm, the student still passed.

In some cases, the weight may be given not as a percent, but a number may be assigned to each section of the examaination

Homework assignments: 1
Quizzes: 1
Midterm: 2
Final exam: 3

For the same example above, weighted average =
1 × 45 + 1 × 50 + 2 × 65 + 3 × 95 / 7

weighted average =
45 + 50 + 130 + 285 / 7

weighted average =
510 / 7
= 72.85

### Weighted average formulas

When the weight is expressed as a percent, the formula can be expressed as shown below:

weighted average = percent1 × x1 + percent2 × x2 + ... + percentn × xn

When the weight is expressed as a number, the formula can be expressed as shown below:

weighted average =
weight1 × x1 + weight2 × x2 + ... + weightn × xn / weight1 + weight2 + ... + weightn

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