Statistics & Probability for Competitive Exam Success

Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

Q. In a survey, 70% of people prefer tea over coffee. If 200 people were surveyed, how many prefer tea? (2019)

A. 140
B. 150
C. 160
D. 170

Solution

Number of people preferring tea = 70% of 200 = 0.7 * 200 = 140.

Correct Answer: A — 140

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Q. In a survey, the ages of 15 participants are: 22, 22, 23, 24, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 30. What is the mode?

A. 22
B. 24
C. 27
D. 30

Solution

The mode is 30, as it appears 3 times, which is more than any other age.

Correct Answer: D — 30

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Q. In a survey, the ages of 15 participants are: 22, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 30, 30. What is the mode of the ages?

A. 23
B. 25
C. 28
D. 30

Solution

The mode is 30, as it appears most frequently (3 times) in the data set.

Correct Answer: D — 30

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Q. In a survey, the number of languages spoken by individuals is recorded as follows: 1, 2, 2, 3, 3, 3, 4. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 3, as it appears three times in the data set.

Correct Answer: C — 3

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Q. In a survey, the number of languages spoken by participants is recorded as follows: 1, 2, 2, 3, 3, 3, 4, 5. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 3, as it appears 3 times, more than any other number.

Correct Answer: C — 3

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Q. In a survey, the number of siblings reported by participants is: 0, 1, 2, 1, 2, 2, 3. What is the mode?

A. 0
B. 1
C. 2
D. 3

Solution

The mode is 2, which appears 3 times in the data set.

Correct Answer: C — 2

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Q. In the data set 1, 2, 2, 3, 4, 4, 4, 5, 5, what is the mode?

A. 1
B. 2
C. 4
D. 5

Solution

The mode is 4, as it appears most frequently (three times) in the data set.

Correct Answer: C — 4

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Q. In the data set 9, 10, 10, 11, 12, 12, 12, 13, what is the mode?

A. 9
B. 10
C. 11
D. 12

Solution

The mode is 12, as it appears 3 times, which is more than any other number.

Correct Answer: D — 12

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Q. In the data set: 2, 3, 3, 4, 4, 5, 5, 5, what is the mode?

A. 2
B. 3
C. 4
D. 5

Solution

The mode is 5, as it appears most frequently (three times) in the data set.

Correct Answer: D — 5

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Q. In the following data set: 1, 2, 2, 3, 3, 4, 4, 4, what is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 4, as it appears most frequently (three times) in the data set.

Correct Answer: D — 4

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Q. In the following data set: 4, 4, 4, 5, 5, 6, 7, 8, what is the mode?

A. 4
B. 5
C. 6
D. 7

Solution

The mode is 4, as it appears most frequently (three times) in the data set.

Correct Answer: A — 4

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Q. In the following set of scores: 45, 50, 50, 60, 70, 70, 70, 80, what is the mode?

A. 45
B. 50
C. 60
D. 70

Solution

The mode is 70, as it appears 3 times, which is more than any other score.

Correct Answer: D — 70

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Q. In the set of numbers 5, 5, 6, 7, 8, 8, 8, 9, what is the mode?

A. 5
B. 6
C. 7
D. 8

Solution

The mode is 8, as it appears 3 times, which is more than any other number.

Correct Answer: D — 8

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Q. The ages of a group of people are: 22, 25, 22, 30, 25, 22, 28. What is the mode of their ages?

A. 22
B. 25
C. 28
D. 30

Solution

The mode is 22, as it appears 3 times, more than any other age.

Correct Answer: A — 22

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Q. The average of 10, 20, 30, and x is 25. What is the value of x?

A. 20
B. 30
C. 40
D. 50

Solution

Mean = (10 + 20 + 30 + x) / 4 = 25. Solving gives x = 50.

Correct Answer: C — 40

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Q. The average of 4, 6, 8, and x is 7. What is the value of x?

A. 6
B. 8
C. 10
D. 12

Solution

Mean = (4 + 6 + 8 + x) / 4 = 7.\n\n18 + x = 28\n\nx = 28 - 18 = 10.

Correct Answer: C — 10

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Q. The average of five consecutive integers is 12. What is the smallest of these integers?

A. 10
B. 11
C. 12
D. 13

Solution

Let the integers be x, x+1, x+2, x+3, x+4.\n\nMean = (5x + 10) / 5 = 12\n\n5x + 10 = 60\n\n5x = 50\n\nx = 10.

Correct Answer: B — 11

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Q. The average of five numbers is 20. If one number is excluded, the average of the remaining numbers becomes 18. What is the excluded number?

A. 22
B. 24
C. 20
D. 18

Solution

Total of five numbers = 5 * 20 = 100. Total of remaining four = 4 * 18 = 72. Excluded number = 100 - 72 = 28.

Correct Answer: A — 22

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Q. The average of five numbers is 20. If one number is removed, the average becomes 18. What is the number removed?

A. 22
B. 24
C. 20
D. 18

Solution

Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Number removed = 100 - 72 = 28.

Correct Answer: A — 22

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Q. The average of three consecutive integers is 20. What are the integers?

A. 19, 20, 21
B. 18, 19, 20
C. 20, 21, 22
D. 17, 18, 19

Solution

Let the integers be x, x+1, x+2. (x + (x + 1) + (x + 2)) / 3 = 20. Therefore, 3x + 3 = 60, so x = 19.

Correct Answer: A — 19, 20, 21

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Q. The average of three numbers is 15. If one number is increased by 5, what will be the new average?

A. 15
B. 16
C. 17
D. 18

Solution

Total of three numbers = 3 * 15 = 45.\n\nNew total = 45 + 5 = 50.\n\nNew average = 50 / 3 = 16.67.

Correct Answer: B — 16

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Q. The average of two numbers is 30. If one number is 20, what is the other number?

A. 40
B. 50
C. 60
D. 70

Solution

Mean = (20 + x) / 2 = 30.\n\n20 + x = 60\n\nx = 60 - 20 = 40.

Correct Answer: A — 40

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Q. The following data represents the number of books read by students in a month: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 3

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Q. The following data represents the number of books read by students in a month: 4, 5, 6, 5, 4, 5, 7, 8, 5. What is the mode?

A. 4
B. 5
C. 6
D. 7

Solution

The mode is 5, as it appears 4 times, more than any other number.

Correct Answer: B — 5

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Q. The following data set has the numbers: 2, 3, 4, 4, 5, 5, 5, 6, 7. What is the mode of this data set? (2020)

A. 4
B. 5
C. 6
D. 7

Solution

The number 5 appears most frequently (3 times), so the mode is 5.

Correct Answer: B — 5

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Q. The following data set represents the ages of participants in a survey: 22, 25, 22, 30, 25, 22, 28. What is the mode?

A. 22
B. 25
C. 28
D. 30

Solution

The mode is 22, as it appears most frequently (three times) in the data set.

Correct Answer: A — 22

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Q. The following data shows the number of goals scored by a team in 7 matches: 1, 2, 2, 3, 2, 4, 5. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 2, as it appears 3 times, more than any other number.

Correct Answer: B — 2

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Q. The following data shows the number of pets owned by families: 0, 1, 1, 2, 2, 2, 3, 4. What is the mode?

A. 0
B. 1
C. 2
D. 3

Solution

The mode is 2, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 2

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Q. The following data shows the number of pets owned by families: 1, 1, 2, 2, 3, 3, 3, 4. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 3

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Q. The following numbers represent the number of books read by students: 1, 2, 2, 3, 4, 4, 4, 5. What is the mode?

A. 2
B. 3
C. 4
D. 5

Solution

The mode is 4, as it appears three times, which is more than any other number.

Correct Answer: C — 4

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Statistics & Probability

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