Word Problems
(Statistics)
Practice Exercise
Very Easy (Difficulty Level-1):
1. If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference between the greatest and least of the five integers?
(a) 4
(b) 4k
(c) 4k + 4
(d) 4 – 4k
(e) 4k2 – 4k
2. If the average (arithmetic mean) of b and c is 5, and the average of c and d is 10, then b – d =
(a) Cannot be determined
(b) -5
(c) -10
(d) -15
(e) -20
3. If the average (arithmetic mean) of seven consecutive integers is k + 2, then the product of the greatest and least integer is
(a) k2 – 9
(b) k2 – 2k + 1
(c) k2 + 4k – 12
(d) k2 + 6k + 9
(e) k2 + 4k – 5
4. What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?
(a) 190
(b) 195
(c) 200
(d) 205
(e) 210
5. If the average (arithmetic mean) of x, y, and 20 is 11, then the average of 2x + 3, 2y – 4, and 8 is?
(a) 11
(b) 12
(c) 13
(d) 14
(e) 15
Here’s a GRE question:
6. If x is an integer, which of the following could be the median of the set {6, 5, x, 6, 3, x}?
Indicate all possible medians.
(a) 3
(b) 3.5
(c) 4
(d) 4.5
(e) 5
(f) 5.5
(g) 6
Easy (Difficulty Level-2):
7. In a certain course, Ali received an average score of 82 for this first 2 tests, 76 for this third test and 92 for this fourth test. What grade must he receive on this next test if he wants an average of 86 for all 5 tests.
(A) 92
(B) 94
(C) 96
(D) 98
(E) 100
8. The average (arithmetic mean) of two numbers is 4x. If one of the numbers is y, then the value of the other number is
(a) x – 4y
(b) 4x + 4y
(c) 8x – 4y
(d) 4y – 8x
(e) 8x – y
9. Jack has 5 cats and 1 dog. If the dog’s weight is 3 times the average (arithmetic mean) weight of the cats, then the dog’s weight is what fraction of the total weight of all 6 animals?
10. If 4⁄w + 4⁄x = 4⁄y and wx = y, then the average (arithmetic mean) of w and x is
(a) 1⁄2
(b) 1
(c) 2
(d) 4
(e) 8
11. The average (arithmetic mean) of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?
(a) 1
(b) 19
(c) 29
(d) 30
(e) 33
12. 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) 1000
(D) 1200
(E) 1500
Easy (Difficulty Level-3):
13. Set A: {x, x, x, y, y, y, 3x+y, x – y}
If the median of set A is 10 and 0 < x < y, what is the range of set A?
14. In a certain class, x students are 10 years old, and the remaining y students are 11 years old. What is the average (arithmetic mean) age of all students in the class?
15. What is average (arithmetic mean) of w, x, and y, if:
w + x = -4
x + y = 25
y + w = 15
16. Three members of a track team have weights that range from 110 to 135 pounds. Which of the following cannot possibly be the average of the three trackmen?
(A) 117
(B) 119
(C) 122
(D) 125
(E) 126
17. The average of n numbers is a. If x is subtracted from each number, then average of n numbers becomes?
(A) ax⁄n
(B) an⁄x
(C) an – x
(D) n – x
(E) a – x
18. Positive integers a,b,c,d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d – b = 3, then what is the greatest possible range of the five numbers?
(a) 12
(b) 17
(c) 18
(d) 19
(e) 20
Hard (Difficulty Level-4):
19. In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls?
20. Ten students wrote a test, and the distribution of scores is shown on the frequency table. If the average (arithmetic mean) score is 62, what is the value of x?
(a) 62
(b) 65
(c) 71
(d) 76
(e) 83
21. If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
22. Set X={a, b, c}, where a < b < c. If the average (arithmetic mean) of a and b is 3x – 13, and the average of b and c is 3x+11, what is the range of set X?
23. Which of the following sets of numbers has the greatest standard deviation?
(a) 10, 11, 12
(b) -3, -4, -5
(c) -2, 0, 2
(d) 5.1, 5.2, 5.3
(e) 20, 22, 22.5
24. In a population of chickens, the average (arithmetic mean) weight is 6.3 pounds, and the standard deviation is 1.2 pounds. Which of the following weights (in pounds) are within 1.5 units of standard deviation of the mean?
Indicate all weights.
(a) 4.4
(b) 4.6
(c) 5.1
(d) 5.2
(e) 6.9
(f) 7.6
(g) 7.7
(h) 8.2
Very Hard & Tricky (Difficulty Level-5):
25. Sam earned a $2000 commission on a big sale, raising his average commission by $100. If Sam’s new average commission is $900, how many sales did he make?
26. There are 10 employees in an office. The table shows how many employees have 0,1,2 or 3 pets. If the office manager were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?
(a) 3
(b) 4
(c) 5
(d) 6
(e) 7
27. If a set of numbers is normally distributed with a mean of 82 and a standard deviation of 6, approximately what percent of the numbers are greater than 76 and less than 94?
Give your answer to the nearest integer.
28. In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. What is the mean of the set?
Give your answer to the nearest 0.1
29. Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?
(a) -100 and -100
(b) -10 and -10
(c) 0 and 0
(d) 0 and 20
(e) 10 and 10
30. If the mean of set A is 6.8 and the standard deviation is 3.6 then how many elements of set A are within 1 unit of standard deviation of the mean? A = {2, 9, 2, 6, 9, 10, 7, 4, 5, 14}
(a) 3
(b) 4
(c) 5
(d) 6
(e) 7
Answer Sheet:
1. A
2. C
3. E
4. D
5. A
6. C, D, E and G
7. D
8. E
9. 3⁄8
10. A
11. E
12. C
13. 40
14. (10x + 11y)⁄(x + y)
15. 6
16. A
17. E
18. C
19. 1⁄5
20. B
21. 48
22. 48
23. C
24. B, C, D, E, F and G
25. 12
26. D
27. 82
28. 9.8
29. E
30. E