The document provides practice problems for calculating averages. It includes examples of finding the average of sets of numbers, word problems involving averages, problems where part of the data is excluded, finding missing values, averages of algebraic expressions, and problems involving how averages change when values are added or subtracted from numbers in the set. Students are to show their work and solutions on paper and view the document as a full screen slideshow.

1. AveragesRecord your work and answers on a piece of paper.
These practice problems are due at the end of the
period. No late work will be accepted.
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2. Find the average:
Example:
Find the average of the
following set of values:
89, 66, 98, 75, 96, 86
Show your work on paper:
Find the average of the
following set of values:
1. 12, 14, 22
2. 61, 71, 74, 89, 90
3. 40, 55, 56, 59, 64, 74
4. 110, 152
89 + 66 + 98 + 75 + 96 + 86 = 510
510 / 6 = 85
because there
were 6 values
1. Add all values.
2. Divide by the number of values.

3. Basic Average Word Problems
5. The daily totals of lunch customers served at the
Sunshine Café last Monday through Saturday were
256, 189, 204, 179, 166, and 218. What was the
average number of lunch customers served each
day?
A. 1,212
B. 256
C. 202
D. 197
E. 173
6. A group of friends were comparing the number of
cards in their baseball card collection. The number
of cards is indicated in the table below.
Friend A B C D E
Cards 30 110 70 200 70
What is the average number of baseball cards in the
collection of the 5 friends?
A. 70
B. 82
C. 96
D. 102.5
E. 120
7. As part of a school report on the cost of gasoline,
Raquel wants to find the average cost of purchasing
a gallon of regular unleaded gasoline from local gas
stations. She surveys 4 stations and finds the cost
per gallon of regular unleaded gas from he 4
stations to be $2.45, $2.50, $2.49, and $2.56,
respectively. Using this data, what is the average
cost of purchasing one gallon of regular unleaded
gasoline from these 4 gas stations?
A. $2.55
B. $2.53
C. $2.50
D. $2.49
E. $2.45

4. Find the average from part of the data:
Example:
Geoff made the following scores in a game:
12, 13, 15, 9, 10, 15, 11, 15, 18, 29, 8. The
highest score and lowest score are not
counted in the set. What is the average of
the set without the highest score and
lowest score?
Show your work on paper:
Find the average of the following set
of values excluding the highest
number:
8. 68, 37, 54, 71, 45
9. 19, 21, 25, 17
10. 82, 95, 66, 59, 84, 74
9 + 10 + 11 + 12 + 13 + 15 + 15+ 15 + 18
= 118
118 / 9 = 13
1. Figure out which data to use.
2. Find the average.
8, 9, 10, 11, 12, 13, 15, 15, 15, 18, 29

5. Find the average from part of the data
problems
11. Mr. Polk does no count the
highest and lowest scores when
determining a student’s final
grade. A student has the
following set of scores: 70, 87, 80,
86, 88, 93, 84. If Mr. Polk does
not include the highest and
lowest scores, what is the
average score for the set?
A. 84
B. 85
C. 86
D. 87
E. 88
12. To determine a student’s overall
test score for the semester, Ms.
Lopez throws out the lowest test
score and takes the average of
the remaining test scores. Victor
earned the following test scores
in Ms. Lopez’s class this semester:
62, 78, 83, 84, and 93. What
overall test score did Victor earn
in Ms. Lopez’s class this
semester?
A.67.6
B. 80.0
C. 83.0
D. 83.5
E. 84.5

6. Find a missing value:
Example:
The average of 3 numbers is 45. If 2 of
the numbers are 35 and 45, what is
the third number?
Show your work on paper:
Find the missing value in
each set:
13. 5, 10, ___.
Average = 9
14. 20, 24, 29, ___.
Average = 21
15. 43, 45, 56, 59, 64, ___
Average = 50
35, 45, ____
Average: 45
45 * 3 = 135
because there
were 3 values
1. Calculate the number all the numbers should add up to.
2. Subtract to find the missing value.
135 – 35 = 100 – 45 = 55

7. Find a Missing Value Problems16. If the average of a and -5 is 10, then a=
A. 25
B. 15
C. 5
D. -5
E. -15
17. George has taken 5 tests in math class and scored 98,
78, 87, 99, and 83. If each math test has 100 points
possible, what is the lowest score George can
receive on the next test to have at least a 92
average?
A. 89
B. 92
C. 95
D. 100
E. George cannot average 92 on the 6 tests.
18. Zoe bought three fish at the pet store. Two of the fish
were $7.00 each. If the average cost of the three
fish was $9.00, how much was the third fish?
A. $7.00
B. $7.67
C. $9.00
D. $13.00
E. $16.00
19. A student has earned the following scores on four
100-point tests this marking period: 63, 72, 88, and
91. What score must the student earn on the fifth
and final 100-point test of the marking period to
earn an average test grade of 80 for the five tests?
A. 79
B. 86
C. 89
D. 94
E. The student cannot earn an average of 80.
20. In a certain course, Lily received an average score of
82 for her first 2 tests, 76 for her third test, and 92
for her fourth test. What grade must she receive on
her next test if she wants an average of 86 for all 5
tests?
A. 92
B. 94
C. 96
D. 98
E. 100

8. Find the average of algebraic terms:
Example:
What is the average of n,
n + 1, n + 2, and n + 3?
Show your work on paper:
Find the average of the
following set of values:
21. k + 1, k + 3, k + 5
22. 2m, 3m, 4m, 7m, 9m
n + n + 1 + n + 2 + n + 3 = 4n + 6
(4n + 6) / 4 = 1n + 1.5
because there
were 4 values
1. Add all values by combining like terms.
2. Divide everything by the number of values.

9. Average of Algebraic Terms
23. What is the average of
3x + 2, 4x + 1, and 2x?
A. 2x
B. 3x
C. 3x + 1
D. 3x + 2
E. 9x + 3
24. If the average of x + 2, x
+ 4, and x + 6 is 0, then x
=
A. -4
B. -3
C. -2
D. -1
E. 0

10. Problems with changing averages:
Example:
The average of 6 numbers is 6.
If 3 is subtracted from each
of 4 of the numbers, what is
the new average?
6, 6, 6, 6, 6, 6
3 + 3 + 3 + 3 + 6 + 6= 24
24 / 6 = 4
1. Create an easy set of numbers that works.
2. Change the numbers according to the problem.
3, 3, 3, 3, 6, 6

11. Problems with Changing Averages
25. The average of 8
numbers is 10. If 4 is
added to 5 of the
numbers, what is the
new average?
A. 9
B. 10
C. 12
D. 14
E. 15
26. The average of 3
numbers is 21. If 9 is
subtracted from one of
the numbers, what is the
new average?
A. 9
B. 12
C. 18
D. 21
E. 24