Weighted Average Examples: 43 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Weighted Average.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

A weighted average is an average in which different values contribute unequally based on their assigned weights, reflecting the relative importance or frequency of each value. Unlike a simple average where all values count equally, a weighted average gives more influence to values with larger weights.

Your final grade: exams count 60%, homework 40% — not every assignment counts equally.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Weighted Average asks what single value best stands for the center of the data, then checks whether that value is fair for the situation.

Common stuck point: Students often know a procedure related to weighted average but skip the recognition step: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I need one number that represents the center of the data, and have I checked whether extreme values change that choice?

Worked Examples

Example 1

medium

A student got

85, 92, 78

on three quizzes weighted

2, 3, 1

respectively. What is the weighted average quiz score?

Answer

\frac{524}{6} \approx 87.33

First step

Weighted sum:

2 \cdot 85 + 3 \cdot 92 + 1 \cdot 78 = 170 + 276 + 78 = 524

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Example 2

medium

In a course, homework counts

20\%

, midterm

30\%

, final

50\%

. A student scored

90, 75, 82

. Compute the final grade.

Example 3

hard

A student needs a course average of

85

. So far: homework

20\%

90

, midterm

30\%

80

. The final exam counts

50\%

. What score is needed on the final to reach

85

overall?

Example 4

hard

A weighted average of two values

a

and

b

with weights

w_a

and

w_b

equals

a

exactly. What does that tell you about

w_b

Example 5

hard

Two groups have means

50

and

80

. Their combined weighted average is

65

. If the first group has

30

members, how many are in the second?

Example 6

challenge

Two schools combined have an average test score of

77

. School A averages

80

with

120

students. School B averages

72

. How many students does school B have?

Example 7

hard

A teacher wants final grades to weight homework, midterm, and final at

0.2, 0.3, 0.5

. A student got

70, 80, x

. The teacher wants the final grade to be exactly

80

. What must

x

be?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Write the formula for a weighted average.

Example 2

easy

Two values

4

and

10

have equal weights. What is their weighted average?

Example 3

easy

A grade is

80

(weight

2

) and

90

(weight

1

). Compute the weighted sum

\sum w_i x_i

Example 4

easy

Weights are

2

and

1

. What is the total weight

\sum w_i

Example 5

easy

Using weighted sum

250

and total weight

3

, find the weighted average.

Example 6

easy

If exams count

60\%

and homework

40\%

, do all assignments count equally?

Example 7

easy

A weighted average uses weights that are all the same. What simpler quantity does it equal?

Example 8

easy

Should the weight of a value be confused with the value itself?

Example 9

medium

A course grade: exam

90

(weight

0.6

), homework

80

(weight

0.4

). Find the weighted average.

Example 10

medium

Test scores

70, 80, 90

have weights

1, 2, 3

. Compute the weighted average.

Example 11

medium

A class has

10

students averaging

80

and

20

students averaging

95

. Find the combined (weighted) average.

Example 12

medium

An investment returns

10\%

on $2000 and

4\%

on $3000. What is the weighted average return?

Example 13

medium

A student needs a course average of

90

. Exams (weight

0.7

) average

88

; homework (weight

0.3

) averages

x

. The total is exactly

90

when... actually compute the homework average needed.

Example 14

medium

A GPA uses grade points

4, 3, 4

with credit weights

3, 4, 2

. Compute the GPA.

Example 15

medium

Why can't you just average

50\%

and

90\%

to get the overall pass rate of two groups of different sizes?

Example 16

medium

Values

20

and

40

have weights

w

and

1

. For what weight

w

does the weighted average equal

25

Example 17

medium

Quiz scores

6, 8, 10

have weights

3, 1, 1

. Compute the weighted average.

Example 18

challenge

Two classes: one of

15

students averaging

70

, another of

25

students averaging

86

. Find the overall average.

Example 19

challenge

A blend mixes

3

kg of coffee at $8/kg with

2

kg at $13/kg. Find the price per kg of the blend.

Example 20

challenge

Show that if all weights are doubled, the weighted average is unchanged. Give the key reason.

Example 21

easy

Find the weighted average of

50

(weight

1

) and

100

(weight

1

Example 22

easy

Compute the weighted sum

\sum w_i x_i

for

x = (8, 10)

with

w = (3, 2)

Example 23

easy

Using weighted sum

44

and total weight

5

, what is the weighted average?

Example 24

easy

Compute the weighted average of

20

(weight

0.5

) and

40

(weight

0.5

Example 25

easy

Two values

60

and

90

have weights

1

and

2

. Which weighted average is closer to:

60

90

Example 26

medium

A test grade is

70

(counts

25\%

), midterm

80

(counts

35\%

), final

90

(counts

40\%

). Find the weighted average.

Example 27

medium

A school has

200

students at grade-level average

75

and

300

students at grade-level average

85

. Find the schoolwide (weighted) average.

Example 28

medium

A car drives

100

miles at

40

mph and

100

miles at

60

mph. What is the (time-weighted) average speed for the whole trip?

Example 29

medium

A shop sells

50

shirts at $20 each,

30

shirts at $30 each, and

20

shirts at $50 each. What is the average price per shirt sold?

Example 30

medium

A GPA uses credits as weights: A (

4.0

3

credits), B (

3.0

4

credits), A (

4.0

3

credits). Compute the GPA.

Example 31

hard

A student has

\$5000

3\%

interest and

\$2000

7\%

interest. What is the (dollar-weighted) average interest rate?

Example 32

hard

A truck mixes

400

kg of alloy at

20\%

copper with

600

kg at

35\%

copper. What is the copper percentage of the mix?

Example 33

hard

In a survey,

60\%

500

respondents rated a product

4/5

stars, and the rest rated it

3/5

. What is the average rating?

Example 34

hard

A portfolio holds three stocks with values $2000, $3000, $5000 and returns

8\%, 12\%, 6\%

. What is the portfolio return?

Example 35

medium

A bag has

5

apples averaging

\$0.40

each and

10

oranges averaging

\$0.60

each. What is the average price per fruit?

Example 36

hard

A class of

25

students has a mean test score of

82

. A new student joins with a score of

58

. What is the new class mean?

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Related Concepts

Mean as Fair Share Expected Value Linear Regression

Background Knowledge

These ideas may be useful before you work through the harder examples.

mean fair sharestat expected value