Mean as Fair Share Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mean as Fair Share.

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

Concept Recap

The mean (average) represents what each person would get if the total were divided equally among everyone. It is calculated by adding all values and dividing by the count, giving a single number that summarizes the center of the data.

Imagine 3 friends have 2, 4, and 9 candies. If they pool all candies (15 total) and share equally, each gets 5. That's the mean! It's the 'fair share' - what everyone would have if things were perfectly even.

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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: Mean as Fair Share 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 mean as fair share 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?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Mean vs Median Mistakes

Worked Examples

Example 1

medium

A class of

24

students has mean test score

78

. After a new student joins with score

103

, find the new mean.

Answer

79

First step

Old total

= 24\times 78 = 1872

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Example 2

medium

A car drives

60

mph for

2

h and

80

mph for

3

h. Find the mean speed across all

5

hours.

Example 3

hard

The mean of

n

numbers is

20

. Adding the number

50

raises the mean to

22

. Find

n

Example 4

challenge

The mean of nine numbers is

50

. Adding two more numbers raises the mean to

55

. Find the mean of the two added numbers.

Example 5

easy

Five friends have 3, 7, 5, 10, and 5 sweets respectively. If they share all the sweets equally, how many does each person get?

Example 6

medium

A student scores 72, 85, 90, and 69 on four tests. What score does she need on a fifth test to have a mean of 80?

Practice Problems

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

Example 1

easy

Find the mean of

4, 6, 8

Example 2

easy

Three friends have

2, 4, 9

candies. If shared equally, how many each?

Example 3

easy

Find the mean of

10, 20, 30, 40

Example 4

easy

Find the mean of

7, 7, 7

Example 5

easy

A student scored

80, 90, 100

on three tests. Find the mean score.

Example 6

easy

Find the mean of

5, 15

Example 7

easy

Find the mean of

0, 0, 6

Example 8

easy

Find the mean of

12, 18

Example 9

medium

The mean of

4

numbers is

10

. Three of them are

8, 9, 12

. Find the fourth.

Example 10

medium

A class of

20

students averages

75

. A new student scores

96

. Find the new mean.

Example 11

medium

The mean of

6, 8, x, 14

10

. Find

x

Example 12

medium

Two groups:

5

scores averaging

8

and

3

scores averaging

16

. Find the combined mean.

Example 13

medium

Five numbers average

20

. If each number increases by

4

, find the new mean.

Example 14

medium

Six numbers average

9

. One value,

4

, is removed. Find the new mean of the remaining five.

Example 15

medium

A team's mean weight is

60

kg over

4

players. A

90

kg player joins. Find the new mean.

Example 16

medium

If the mean of

a, b, c

7

, what is

a+b+c

Example 17

challenge

Seven numbers average

12

. Removing one number drops the average of the rest to

11

. Find the removed number.

Example 18

challenge

A list of

n

numbers averages

10

. Adding the number

40

raises the average to

12

. Find

n

Example 19

challenge

Numbers

1,2,3,\dots,k

have mean

5.5

. Find

k

Example 20

medium

Four numbers average

15

. Three are

10, 12, 20

. Find the fourth.

Example 21

easy

Find the mean of

2, 4, 6

Example 22

easy

Four kids have

3, 5, 7, 9

stickers. Find the mean.

Example 23

easy

Find the mean of

1, 1, 4

Example 24

easy

Find the mean of

0, 4, 8

Example 25

easy

Find the mean of

11, 13

Example 26

easy

Five test scores were

70, 75, 80, 85, 90

. Find the mean.

Example 27

easy

Six pencils cost

\$1, \$2, \$2, \$3, \$4, \$6

at six stores. What is the mean price?

Example 28

medium

The mean of five numbers is

12

. Four of them are

10, 11, 13, 14

. Find the fifth.

Example 29

medium

Find the mean of

7, 14, 21, 28, 35

Example 30

medium

The mean of

x, x+2, x+4

20

. Find

x

Example 31

medium

Tom scored

84, 78, 92

on three tests. What score does he need on the fourth to raise his mean to

85

Example 32

medium

Group A has

4

students with mean

90

. Group B has

6

students with mean

80

. Find the combined mean.

Example 33

medium

The mean weight of

5

boxes is

12

kg. One box weighing

20

kg is removed. Find the new mean.

Example 34

medium

The mean of

a, b, c, d

15

. The mean of

a, b

12

. Find the mean of

c, d

Example 35

hard

A teacher's class of

30

has mean score

74

. After tossing the lowest score, the mean of the remaining

29

becomes

76

. What was the dropped score?

Example 36

hard

Five distinct positive integers have mean

7

and the smallest is

3

. What is the largest possible value of the largest integer?

Example 37

hard

If every value in a data set is increased by

5

, what happens to the mean?

Example 38

hard

If every value in a data set is doubled, what happens to the mean?

Example 39

hard

Six employees have a mean salary of

\$40{,}000

. The owner (

\$200{,}000

) joins the average. Find the new mean.

Example 40

easy

Four boxes contain 12, 8, 14, and 6 apples. Find the mean number of apples per box.

Example 41

easy

Three jars hold 9, 12, and 6 marbles. How many marbles must move from the second jar to the third jar so that all three jars have the same number?

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Related Concepts

Weighted Average