Download 1. If the average (arithmetic mean)

Mean, Median, Mode (SAT Style)
Name ________________________
1. If the average (arithmetic mean) of a and -5 is 10, then a =
(A) 25
(B) 15
(C) 5
(D) -5
(E) -15
2. The average (arithmetic mean) of 6 consecutive integers is 18½. What is the average of the first
5 of these integers?
(A) 12 ½
(B) 15
(C) 16
(D) 17 ½
(E) 18
3. What is the average (arithmetic mean)
weight of the five people whose weights are
listed in the table to the right?
(A) 152
(B) 153
(C) 153.5
(D) 154
(E) 155
Name
Justin
Glenn
Shaun
Gerald
Greg
Weight
(Pounds)
150
153
154
157
151
4. A certain store stocks 5 different brands of ice cream, and sells a pint of each for $2.75, $3.25,
$2.50, $3.25, and $3.00, respectively. What is the positive difference between the mode price and
the median price?
(A) $0.05
(B) $0.25
(C) $0.30
(D) $0.50
(E) $0.75
5. The average (arithmetic mean) of 3 numbers is 45. If 2 of the numbers are 35 and 45, what is
the third number?
(A) 30
(B) 40
(C) 45
(D) 50
(E) 55
6. If the average (arithmetic mean) of b and 2 is equal to the average of b, 3, and 4, what is the
value of b?
(A) 2
(B) 4
(C) 8
(D) 10
(E) 16
7. The average (arithmetic mean) of 30, 50, and 70 is 15 more than the average of 40, 60, and what
number?
(A) 65
(B) 55
(C) 35
(D) 15
(E) 5
8. A violinist practices 1 hour a day from Monday through Friday. How many hours must she practice
on Saturday in order to average 2 hours a day for the 6-day period?
9. The average (arithmetic mean) of 6 numbers is 6. If 3 is subtracted from each of 4 of the
numbers, what is the new average?
(A)
1½
(B) 2
(C) 3
(D) 4
(E) 4 ½
10. What is the average (arithmetic mean) of n, n + 1, n +2, and n + 3?
(A) n + 1
(B) n + 1.5
(C) n + 2
(D) n + 2.5
(E) n + 6
11. The average (arithmetic mean) of two numbers is 3n – 4. If one of the numbers is n, then the
other number is:
(A) 2n – 4
(B) 3n – 4
(C) 5n – 8
(D) 5n + 8
(E) 6n – 8
12. If the average (arithmetic mean) of x + 2, x + 4, and x + 6 is 0, then x =
(A) -4
(B) -3
(C) -2
(D) -1
(E) 0
13. In a certain class there are 12 boys and 18 girls. If the class average score for an algebra exam
is 90 and the boys’ average score is 87, what is the girls’ average score?
(A) 88.5
(B) 91
(C) 92
(D) 93
(E) 94.5
14. What is the sum of the median, mode, and range of the set {-1, 0, 1, 1, 2, 0, 0, 2}?
15. The average (arithmetic mean) of a set of 4 numbers is 8.75. When a fifth number is
introduced to the set, the average of the set becomes 8. What is the fifth number?
(A) -3
(B) 5
(C) 8.375
(D) 8.6
(E) 10.3
16. If the sum of m integers is 0, which of the following must be true?
I.
II.
III.
(A) I only
(B) II only
m – 1 is an odd number
m + 1 is an even number
The average (arithmetic mean) of the m integers is 0
(C) III only
(D) I and III
(E) II and III
17. Jerry’s average (arithmetic mean) score on the first three of four tests is 85. If Jerry wants
to raise his average by 2 points, what score must he earn on his fourth test?
18. In a certain course, Lily received an average (arithmetic mean) 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 (arithmetic mean) of 86 for all 5 tests?
19. 15 movie theaters average 600 customers per theater per day. If 6 of the theaters close down
but the total theater attendance stays the same, what is the average daily attendance per theater
among the remaining theaters?
(A) 500
(B) 750
(C) 1,000
(D) 1,200
(E) 1,500
20. The average (arithmetic mean) of 6 positive numbers is 5. If the average of the least and
greatest of these numbers is 7, what is the average of the other 4 numbers?
(A) 3
(B) 4
(C) 5
(D)6
(E) 7
21. If the average of 27-x, x-8, and 3x+ 11 is y, what is the average of 2y and 2y/3?
8𝑥+80
4𝑥+40
2𝑥+20
(A) 4x + 40
(B) x+10
(C)
(D)
(E)
3
3
3
22. If the average (arithmetic mean) of t and s is 25 and the average of r and s is 40, what is the
value of r – t ?
(A) 65
(B) 32.5
(C) 30
(D) 15 (E) It cannot be determined from the information given.
23. George drives the first 30 miles of a trip at a constant rate of 40 miles per hour. If he drives
the remaining 75 miles of the trip at a constant rate of 50 miles per hour, what is his average speed
for the entire trip?
24. If the average (arithmetic mean) of 18 consecutive odd integers is 534, what is the least of
these integers?
25. If the average (arithmetic mean) of a, b, and 7 is 13, what is the average of a + 3, b - 5, and 6.
26. The mean quiz score is:
A) 96
B) 97
C) 98
D) 99
This chart is for #26-28
E) 100
27. The median quiz score is:
A) 96
B) 97
C) 98
D) 99
E) 100
28. The mode of the quiz scores is:
A) 96
B) 97
C) 98
D) 99
E) 100
Sandy’s Quiz
Scores
Grade
Number
100
4
98
3
95
2
86
1
Total
10
29. The average (arithmetic mean) of three numbers is 90. The sum of two of the numbers is 150.
What is the value of the third number?
A) 90
B) 100 C) 110 D) 120 E) 130
30. Using the data set, {30,70,40,50,90,40,60}, which of the following statements is correct?
A) median < mean < mode
B) mode < mean < median
D) mean < mode < median
E) median < mean < mode
C) mode < median < mean
31. The average (arithmetic mean) of four consecutive even integers is 5. What is the median of
these four numbers?
The tables to the right show the points scored
by two different basketball players, Jay and
Ed. Ed's average (arithmetic mean) for 4 games
is 2 less than Jay's average for 5 games.
Use the data to the right for questions #32-33
Jay’s Points
20
16
25
15
14
Ed’s Points
15
21
17
?
32. How many points did Ed score during the fourth game?
A) 12 B) 11 C) 10 D) 9
E)8
33. Say that Ed scored 16 points in the fourth game. What should be added to Jay's median score
to equal the median of Ed's scores?
34. Blaire, Chen, Erin, Liz, and Mauro all participate in a 1-mile race. The average (arithmetic mean)
for the times of all girls is 6.5 minutes. If the average time for Blaire, Chen, and Erin is 6.7
minutes, what is the average time for Liz and Mauro?
A) 6.1 minutes B) 6.2 minutes C) 6.3 minutes D) 6.4 minutes E) 6.5 minutes
35. What is the median of the modes in the dataset {-5,4,3,7,2,1,3,4,5,-1,7,8,-4,2,6}?
A) 2
B) 2.5 C) 3
D) 3.5 E) 4
36. The average of x and y is 7, and z = 3x + 2. What is the average of y and z?
A) 2x + 8
B) 2x - 16
C) 2x + 16
D) x - 8
E) x + 8
37. The average of a set of n numbers is x. If each number is increased by y, then what is the
average of the new set of numbers?
A) x
B) y
C) n(x + y)
D) x + y
E) (x + y) / n
38. Mr. Jones administered a test to the
students in each of his three Algebra II
classes. The average (arithmetic mean) of all
the students in his classes was 82.8. What is
the average for his Period 7 class?
39.
a+b+c+d
A) 14
4
# of students
Class average
A) 80
B) 81
Period 1
16
85
C) 82
Period 6
19
80
D) 83
Period 7
15
?
E) 84
= 12. If the average of a, b, c, d, and e is 14, what is the value of e?
B) 16
C) 18
D) 20
E) 22
40. Frank took 4 history tests. Frank earned an 85, 92, and 89 on the first three tests. If Frank's
average (arithmetic mean) for all 4 tests is 91, what did he earn on his last test?
A) 100 B) 99 C) 98 D) 97 E) 96
41. If the average of 6 evenly spaced numbers is x, what is the median of the 6 numbers?
A) x
B) 2x
C) x/2
D) 6x
E) x/6
42. a, b, and c are all positive integers such that a + b+ c = 150,and none of these values are equal to
each other. What is the smallest possible value for the median of a, b, and c?
A. 5
B. 4
C. 3
D. 2
E. 1
43. s and t are positive integers whose average (arithmetic mean) is 9. If s < t, what is the median
of all possible values of 5?
A. 6.5 B. 6
C. 5.5 D. 5
E. 4.5
44. The modes of a set of 9 numbers are x, y, and z, and the average (arithmetic mean) of the 9
numbers is 20. Three of the 9 numbers are 2x + 5, 2y, and 2z - 3. What is the value of 4(x + y + z)?
A. 178 B. 179 C. 180 D. 181 E. 182
45. If c is equal to the sum of a and twice b, which of the following is the average (arithmetic mean)
of a and c?
A) c
B) a + b
C) a
D) b
E) a + c
46. The sum of 10 consecutive integers is 105. What is the median of these 10 integers?
47. The average (arithmetic mean) of five numbers is 10. The sum of three of the numbers is 30.
What is the sum of the other two numbers?
A. 5
B. 10 C. 20 D. 30 E. 40
48. The average of six consecutive positive integers is 14.5. What is the value of the smallest
positive integer?
49. The sum of the heights of six people is 336 inches. No two people are the same height. What is
the mean height of the third and fourth tallest people if the mean and the median height of all six
people are equal?
A. 84
B. 67.2
C. 56
D. 56.5
E. 57
50. Five groups of men, 10 men in each group, have the following average ages: 36,42,32,34, and 40.
What is the sum of the ages of all 50 men?
A. 184
B. 368
C. 552
D. 1,840
E. 3,680
51. Let a represent the arithmetic mean of k numbers whose sum is S. Which of the following is
equal to 1?
𝑎∙𝑘
𝑆∙𝑎
𝑆∙𝑘
𝑘
A)
B)
C)
D) 𝑆 ∙ 𝑎 ∙ 𝑘
E)
𝑆
𝑘
𝑎
𝑎∙𝑆
52. The average (arithmetic mean) of five positive integers is 56.The difference between the
largest and smallest integer is 4. What is the median of the numbers?
A. 55
B. 55.5
C. 56
D. 56.5
E. 57
53. The average of 20, 70, and x is 40. If the average of 20, 70, x, and y is 50, then y =
(A) 100
(B) 80
(C) 70
(D) 60
(E) 30
54. In a certain game, each of 5 players received a score between 0 and100, inclusive. If their
average (arithmetic mean) score was 80, what is the greatest possible number of the 5 players who
could have received a score of 50?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
55. N is a set of numbers whose average (arithmetic mean) is 3. M is a set that is generated by
doubling each number in N. What is the average of the numbers in set M?
(A) 1/3
(B) 2
(C) 3
(D) 6
(E) 9
56. If the areas of two regions are equal and the sum of the areas of the regions is 5, what is the
average (arithmetic mean) of the areas of the two regions?
(A) 0
(B) 5/2
(C) 5/4
(D) 5
(E) 10
57. The average (arithmetic mean) of the test scores of a class of p students is 70, and the
average of the test scores of a class of n students is 92. When the scores of both classes are
combined, the average score is 86.What is the value of p/n ?
58. In a set of eleven different numbers, which of the following CANNOT affect the value of the
median?
(A) Doubling each number
(B) Increasing each number by 10
(C) Increasing the smallest number only
(D) Decreasing the largest number only
(E) Increasing the largest number only
59. The graph to the right shows the effect
of aging on the diameter of the eye pupil.
Based on the graph, what is the best estimate
of the age at which the average diameter of
the eye pupil during the day will equal the
average diameter of the eye pupil at night?
(A) 20
(B) 30
(C) 35
(D) 45
(E) 60
60. Each of 5 people had a blank card on which they wrote a positive integer. If the average
(arithmetic mean) of these integers is 15, what is the greatest possible integer that could be on one
of the cards?
61. In the triangles to the right, what is the
average (arithmetic mean) of u, v, w, x, and y?
(A) 21
(B) 45
(C) 50
(D) 52
(E) 54
62. The average (arithmetic mean) of the weights of 14 books is p pounds. In terms of p, what is
the total weight of the books, in pounds?
(A) 14 + p
(B) p - 14
(C) p/14
(D) 14/p
(E) 14p
63. If the average (arithmetic mean) of x and 3x is 12, what is the value of x?
(A) 2
(B) 4
(C) 6
(D) 12
(E) 24