# Weighted mean

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

The power of weighted average is noticeable with a final exam. 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 growth on a final exam and reward students as a result.

## A real-life example showing how to find the weighted mean

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

Then, find the average score for the quizzes

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

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 examination.

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 mean formulas

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

weighted average = percent

_{1} × x

_{1} + percent

_{2} × x

_{2} + ... + percent

_{n} × x

_{n}
When the weight is expressed as a number, the formula can be expressed as shown below:

Weighted average =

weight_{1} × x_{1} + weight_{2} × x_{2} + ... + weight_{n} × x_{n}
/
weight_{1} + weight_{2} + ... + weight_{n}

Let weighted average =

X and let weight = w

X =

w_{1} × x_{1} + w_{2} × x_{2} + ... + w_{n} × x_{n}
/
w_{1} + w_{2} + ... + w_{n}