Mean as Fair Share Examples in Statistics

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 2424 students has mean test score 7878. After a new student joins with score 103103, find the new mean.

Answer

7979

First step

1
Old total =24×78=1872= 24\times 78 = 1872.

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Example 2

medium
A car drives 6060 mph for 22 h and 8080 mph for 33 h. Find the mean speed across all 55 hours.

Example 3

hard
The mean of nn numbers is 2020. Adding the number 5050 raises the mean to 2222. Find nn.

Example 4

challenge
The mean of nine numbers is 5050. Adding two more numbers raises the mean to 5555. 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 4,6,84, 6, 8.

Example 2

easy
Three friends have 2,4,92, 4, 9 candies. If shared equally, how many each?

Example 3

easy
Find the mean of 10,20,30,4010, 20, 30, 40.

Example 4

easy
Find the mean of 7,7,77, 7, 7.

Example 5

easy
A student scored 80,90,10080, 90, 100 on three tests. Find the mean score.

Example 6

easy
Find the mean of 5,155, 15.

Example 7

easy
Find the mean of 0,0,60, 0, 6.

Example 8

easy
Find the mean of 12,1812, 18.

Example 9

medium
The mean of 44 numbers is 1010. Three of them are 8,9,128, 9, 12. Find the fourth.

Example 10

medium
A class of 2020 students averages 7575. A new student scores 9696. Find the new mean.

Example 11

medium
The mean of 6,8,x,146, 8, x, 14 is 1010. Find xx.

Example 12

medium
Two groups: 55 scores averaging 88 and 33 scores averaging 1616. Find the combined mean.

Example 13

medium
Five numbers average 2020. If each number increases by 44, find the new mean.

Example 14

medium
Six numbers average 99. One value, 44, is removed. Find the new mean of the remaining five.

Example 15

medium
A team's mean weight is 6060 kg over 44 players. A 9090 kg player joins. Find the new mean.

Example 16

medium
If the mean of a,b,ca, b, c is 77, what is a+b+ca+b+c?

Example 17

challenge
Seven numbers average 1212. Removing one number drops the average of the rest to 1111. Find the removed number.

Example 18

challenge
A list of nn numbers averages 1010. Adding the number 4040 raises the average to 1212. Find nn.

Example 19

challenge
Numbers 1,2,3,…,k1,2,3,\dots,k have mean 5.55.5. Find kk.

Example 20

medium
Four numbers average 1515. Three are 10,12,2010, 12, 20. Find the fourth.

Example 21

easy
Find the mean of 2,4,62, 4, 6.

Example 22

easy
Four kids have 3,5,7,93, 5, 7, 9 stickers. Find the mean.

Example 23

easy
Find the mean of 1,1,41, 1, 4.

Example 24

easy
Find the mean of 0,4,80, 4, 8.

Example 25

easy
Find the mean of 11,1311, 13.

Example 26

easy
Five test scores were 70,75,80,85,9070, 75, 80, 85, 90. Find the mean.

Example 27

easy
Six pencils cost $1,$2,$2,$3,$4,$6\$1, \$2, \$2, \$3, \$4, \$6 at six stores. What is the mean price?

Example 28

medium
The mean of five numbers is 1212. Four of them are 10,11,13,1410, 11, 13, 14. Find the fifth.

Example 29

medium
Find the mean of 7,14,21,28,357, 14, 21, 28, 35.

Example 30

medium
The mean of x,x+2,x+4x, x+2, x+4 is 2020. Find xx.

Example 31

medium
Tom scored 84,78,9284, 78, 92 on three tests. What score does he need on the fourth to raise his mean to 8585?

Example 32

medium
Group A has 44 students with mean 9090. Group B has 66 students with mean 8080. Find the combined mean.

Example 33

medium
The mean weight of 55 boxes is 1212 kg. One box weighing 2020 kg is removed. Find the new mean.

Example 34

medium
The mean of a,b,c,da, b, c, d is 1515. The mean of a,ba, b is 1212. Find the mean of c,dc, d.

Example 35

hard
A teacher's class of 3030 has mean score 7474. After tossing the lowest score, the mean of the remaining 2929 becomes 7676. What was the dropped score?

Example 36

hard
Five distinct positive integers have mean 77 and the smallest is 33. What is the largest possible value of the largest integer?

Example 37

hard
If every value in a data set is increased by 55, 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\$40{,}000. The owner ($200,000\$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