Weighted Average - Examples, Exercises and Solutions

Weighted Average: What Does It Really Mean?

A weighted average is an average among numbers with different weights.
Each number has its own weight and, therefore, will affect the weighted average.
Try replacing the word weight with the word importance and in this way its meaning will be better understood.
The numbers are of different importance. One number is more important and another number is less important. It does not mean a large or small number, but simply important.
When a number is more important, it has a greater weight and will have a greater effect on the weighted average.

Detailed explanation

Practice Weighted Average

Question 1

The hotel's rating is determined by several factors, each with a different weight. Here is the rating for the "Happy Tourist" hotel:

Satisfaction: 50% 4.5

Cleanliness: 30% 4

Customer service: 10% 5

Breakfast: 10% 3

What is the hotel's rating?

Question 2

What is Michael's score if he gets 79 on the first exam and 83 on the second, given that the weight of the first test is 30% and that of the second is 70%?

Question 3

A number of hotels are ranked based on various factors, each with a different weight.

This is the rating and weights for the hotel "The Swan Inn":

Satisfaction: 3.5 (45%)
Cleanliness: 4 (30%)
Customer Service: 2 (10%)
Breakfast: 4.5 (10%)
Pool: 1 (5%)

What is the hotel's overall rating?

Question 4

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

4 t-shirts = $45
2 pairs of shorts = $50
3 pairs of pants = $80
2 sweaters = $100
1 coat = $210

What answer should he come up with?

Question 5

What is Monica's average grade if she gets 98 on an assignment that represents 30% and a 95 on an exam that represents 70%?

Examples with solutions for Weighted Average

Exercise #1

The hotel's rating is determined by several factors, each with a different weight. Here is the rating for the "Happy Tourist" hotel:

Satisfaction: 50% 4.5

Cleanliness: 30% 4

Customer service: 10% 5

Breakfast: 10% 3

What is the hotel's rating?

Video Solution

Step-by-Step Solution

In order to determine the hotel rating, we will calculate an average.

Let's remember the weighted average formula:

(value A X weight percentage A)+(value B X weight percentage B)...

First, let's add up all the percentages:

$50\%+30\%+10\%+10\%=100\%$

Now we'll multiply each factor by its weight percentage, convert the percentages to decimal numbers, and add them as follows:

$4.5\times0.5+4\times0.3+5\times0.1+3\times0.1=$

Let's first solve the multiplication exercises:

$2.25+1.2+0.5+0.3=$

We'll add them up and get: 4.25 and that's the hotel rating

Answer

4.25

Exercise #2

What is Michael's score if he gets 79 on the first exam and 83 on the second, given that the weight of the first test is 30% and that of the second is 70%?

Step-by-Step Solution

To solve the weighted average, we will use the following formula:

exam 2 * weight of evaluation 2 + exam 1 * weight of the evaluation 1 = Weighted average

We will place the data in the formula, where the weights will be in decimal numbers:

0.3*79 + 0.7*83 =
23.7+58.1 =

81.8

Answer

$81.8$

Exercise #3

Video Solution

Step-by-Step Solution

In order to determine the hotel rating, we will calculate an average.

Let's remember the weighted average formula:

(value A X weight percentage A)+(value B X weight percentage B)...

First, let's add all the percentages together to make sure we reach 100 percent:

$45\%+30\%+10\%+10\%+5=100\%$

Now we'll multiply each factor by its weight percentage, convert the percentages to decimal numbers, and add them as follows:

$0.45\times3.5+0.3\times4+0.1\times2+0.1\times4.5+0.05\times1=$

Let's solve the multiplication problems first:

$1.575+1.2+0.2+0.45+0.05=$

We'll add them together and get: 3.475 and that's the hotel rating

Answer

3.475

Exercise #4

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

4 t-shirts = $45 <br>2 pairs of shorts =$ 50
3 pairs of pants = $80<br>2 sweaters =$ 100
1 coat = $210

What answer should he come up with?

Video Solution

Answer

$77.5

Exercise #5

What is Monica's average grade if she gets 98 on an assignment that represents 30% and a 95 on an exam that represents 70%?

Video Solution

Answer

$95.9$

Question 1

What is the average grade of the student who got the following:

68 on an exam that represents 40%.

73 on an exam that represents 20%.

94 on a project that represents 15%.

91 on homework that represents 25%.

Question 2

A company is making an advertisement for a new roller coaster and they want to know what the weighted average of its travel speed is.

100 km/h 20%
40 km/h 15%
130 km/h 5%
60 km/h 35%
15 km/h 5%
75 km/h 20%

What is the average speed of the roller coaster?

Question 3

A teacher wants to calculate Gabriel's final weighted average.

The following are Gabriel's exam results:

84 on the test, which is 30% of the final grade.

73 on the exam, which is 15% of the final grade.

87 on the test, which is 35% of the final grade.

92 on the project, which is 20% of the final grade.

What is Gabriel's final average?

Question 4

Ramiro applies to a high school where the average grade required for mathematics is 85.

The following are Ramiro's grades on his maths exams:

92 on a final exam that represents 40%.

78 on a project that represents 15%.

98 on a quiz that represents 10%.

83 on an exam that represents 35%.

Will Ramiro be admitted to the high school and what is his grade average?

Question 5

There are 45 students in a class, 20 of whom have 2 siblings, 15 of whom have 1 sibling, while the rest have no siblings.

How many siblings do the students in the class have on average?

Exercise #6

Video Solution

Answer

$78.65$

Exercise #7

Video Solution

Answer

69.25 km/h

Exercise #8

Video Solution

Answer

$85$

Exercise #9

Video Solution

Answer

Yes, $87.35$

Exercise #10

There are 45 students in a class, 20 of whom have 2 siblings, 15 of whom have 1 sibling, while the rest have no siblings.

How many siblings do the students in the class have on average?

Video Solution

Answer

$1.22$ siblings

Question 1

A durable alloy is made of iron and aluminum.

30% of the alloy is aluminum costing $5 per 100 grams, while 70% is iron costing $17 per 100 grams.

What is the price of 100 grams of the alloy?

Question 2

A factory produces a mix of feathers for filling pillows that constitutes 42% pigeon feathers, 32% goose feathers, and the rest are ostrich feathers.

The prices of the feathers per kg are:

Pigeon - $35

Goose - $95

Ostrich - $72

What is the price per kg of the mix?

Question 3

Ivan rolls a dice and records the results:

$$ 4,3,1,6,5,3,1 $$

What is the average number resulting from the dice rolls?

Question 4

A teacher loses the final exam results of one of his students. Luckily for him, he had already calculated the student's average grade for this year.

Attendance: 95 (10%)
Assessment: 82 (10%)
Assignments: 100 (20%)
Final exam: ??? (60%)

If the student's average is 92, then what grade did he get on his final exam?

Question 5

Below are the data from a factory quality control:

Over 3 days they found 4 defective items each day.

Over 2 days they found 7 defective items each day.

Over 1 day there were no defective items at all.

Over 10 days there were 18 defective items each day.

How many defective items are there on average each day?

Exercise #11

A durable alloy is made of iron and aluminum.

30% of the alloy is aluminum costing $5 per 100 grams, while 70% is iron costing$ 17 per 100 grams.

What is the price of 100 grams of the alloy?