Statistics & Probability for Competitive Exam Success

Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

Q. Calculate the median of the following set: 1, 2, 3, 4, 5, 6, 7, 8. (2020)

A. 4
B. 4.5
C. 5
D. 6

Solution

Arranging the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th numbers: (4 + 5) / 2 = 4.5.

Correct Answer: B — 4.5

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Q. Calculate the median of the following set: 22, 19, 25, 30, 28, 24.

A. 24
B. 25
C. 26
D. 27

Solution

Arrange the numbers: 19, 22, 24, 25, 28, 30. The median is the average of the 3rd and 4th values: (24 + 25) / 2 = 24.5.

Correct Answer: A — 24

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Q. Calculate the variance for the following data: 2, 4, 4, 4, 5, 5, 7, 9. (2019)

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

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 5

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Q. Calculate the variance for the following data: 3, 7, 7, 19. (2022)

A. 20
B. 25
C. 30
D. 35

Solution

Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.

Correct Answer: B — 25

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Q. Calculate the variance for the following data: 5, 7, 9, 11. (2022)

A. 2.5
B. 3.5
C. 4.0
D. 5.0

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.

Correct Answer: B — 3.5

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Q. Calculate the variance of the following numbers: 1, 2, 3, 4, 5. (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

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Q. Consider the data set: 4, 4, 4, 5, 6, 6, 7, 8. What is the mode?

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

Solution

The mode is 4, as it appears 3 times, more than any other number.

Correct Answer: A — 4

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Q. Consider the data set: 5, 6, 7, 8, 8, 9, 9, 10. What is the mode?

A. 5
B. 6
C. 8
D. 9

Solution

The mode is 8 and 9, but since we need to select one, we can choose 8 as it appears first.

Correct Answer: C — 8

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Q. Consider the following data set: 10, 20, 20, 30, 40, 30, 30. What is the mode?

A. 10
B. 20
C. 30
D. 40

Solution

The mode is 30, as it appears three times, which is more than any other number.

Correct Answer: C — 30

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Q. Consider the following data set: 5, 6, 6, 7, 8, 8, 8, 9. What is the mode?

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

Solution

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

Correct Answer: D — 8

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Q. Consider the following numbers: 1, 2, 2, 3, 4, 4, 4, 5. What is the mode?

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

Solution

The mode is 4, which appears most frequently (three times).

Correct Answer: D — 4

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Q. Determine the median of the following numbers: 9, 7, 5, 3, 1.

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

Solution

Arrange the numbers: 1, 3, 5, 7, 9. The median is the middle value, which is 5.

Correct Answer: A — 5

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Q. Determine the median of the following set: 1, 2, 3, 4, 5, 6, 7, 8. (2020)

A. 4
B. 4.5
C. 5
D. 6

Solution

Arrange the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th numbers: (4 + 5) / 2 = 4.5.

Correct Answer: B — 4.5

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Q. Determine the mode of the following data: {1, 2, 2, 3, 4, 4, 4, 5, 5}.

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

Solution

The mode is 4, as it appears 3 times, more than any other number.

Correct Answer: C — 4

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Q. Find the median of the data set: 12, 15, 11, 10, 14, 13. (2020)

A. 11
B. 12
C. 13
D. 14

Solution

First, arrange the numbers: 10, 11, 12, 13, 14, 15. Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers: (12 + 13) / 2 = 12.5.

Correct Answer: C — 13

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Q. Find the median of the data set: 12, 15, 11, 14, 13, 10. (2020)

A. 11
B. 12
C. 13
D. 14

Solution

First, arrange the numbers: 10, 11, 12, 13, 14, 15. Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers: (12 + 13) / 2 = 12.5.

Correct Answer: C — 13

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Q. Find the median of the following data set: 12, 15, 11, 14, 13, 10. (2019)

A. 12
B. 13
C. 14
D. 15

Solution

First, arrange the numbers: 10, 11, 12, 13, 14, 15. The median is the average of the 3rd and 4th numbers: (12 + 13) / 2 = 12.5.

Correct Answer: B — 13

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Q. Find the median of the following set of numbers: 10, 20, 30, 40, 50, 60, 70, 80.

A. 35
B. 40
C. 45
D. 50

Solution

Arrange the numbers: 10, 20, 30, 40, 50, 60, 70, 80. The median is the average of the 4th and 5th values: (40 + 50) / 2 = 45.

Correct Answer: B — 40

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Q. Find the median of the following set of numbers: 9, 3, 6, 2, 8. (2023)

A. 6
B. 7
C. 8
D. 9

Solution

Arrange the numbers: 2, 3, 6, 8, 9. The median is the middle number, which is 6.

Correct Answer: A — 6

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Q. Find the median of the numbers: 12, 15, 10, 20, 18, 25.

A. 15
B. 18
C. 17
D. 20

Solution

Arrange the numbers: 10, 12, 15, 18, 20, 25. Since there are 6 numbers, the median is the average of the 3rd and 4th values: (15 + 18) / 2 = 16.5.

Correct Answer: B — 18

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Q. Find the mode of the following set of numbers: 1, 2, 2, 3, 4, 4, 4, 5, 5.

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

Solution

The mode is 4, as it appears 3 times, which is more than any other number.

Correct Answer: C — 4

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Q. Find the mode of the following set of numbers: 10, 12, 10, 15, 10, 20, 15, 15.

A. 10
B. 12
C. 15
D. 20

Solution

The number 10 appears 3 times and 15 appears 3 times. Since both have the highest frequency, the mode is 10 and 15 (bimodal). However, if only one mode is required, we can take the first one, which is 10.

Correct Answer: C — 15

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Q. Find the mode of the following set of numbers: 10, 12, 10, 15, 10, 20, 15.

A. 10
B. 12
C. 15
D. 20

Solution

The mode is 10, as it appears most frequently (three times) in the data set.

Correct Answer: A — 10

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Q. Find the mode of the following set of numbers: 10, 20, 20, 30, 30, 30, 40, 50.

A. 10
B. 20
C. 30
D. 40

Solution

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

Correct Answer: C — 30

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Q. Find the mode of the following set of numbers: 12, 15, 12, 18, 20, 15, 15, 22.

A. 12
B. 15
C. 18
D. 20

Solution

The mode is 15, which appears 3 times in the data set.

Correct Answer: B — 15

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Q. Find the mode of the following set of numbers: 12, 15, 12, 18, 20, 15, 15.

A. 12
B. 15
C. 18
D. 20

Solution

The number 15 appears most frequently (three times), making it the mode.

Correct Answer: B — 15

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Q. Find the mode of the following set of numbers: 4, 1, 2, 4, 3, 4, 5, 1.

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

Solution

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

Correct Answer: D — 4

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Q. Find the mode of the following set of numbers: 7, 8, 9, 9, 10, 10, 10, 11.

A. 7
B. 8
C. 9
D. 10

Solution

The mode is 10, as it appears 3 times, which is more than any other number.

Correct Answer: D — 10

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Q. Find the mode of the following set of numbers: {10, 12, 10, 15, 10, 20, 15, 15, 25}.

A. 10
B. 15
C. 20
D. 25

Solution

The number 10 appears 3 times and 15 appears 3 times. Both are modes, but since we need to choose one, we can say the mode is 10.

Correct Answer: B — 15

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Q. Find the mode of the following set: {7, 8, 8, 9, 10, 10, 10, 11}.

A. 7
B. 8
C. 9
D. 10

Solution

The mode is 10, which appears 3 times, more than any other number.

Correct Answer: D — 10

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