Statistics & Probability for Competitive Exam Success

Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

Q. The median of the following data set: 3, 7, 9, 15, 20 is?

A. 7
B. 9
C. 15
D. 20

Solution

Arranging the data: 3, 7, 9, 15, 20. Median = 9 (middle value).

Correct Answer: B — 9

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Q. The scores of a class in a test are: 10, 12, 14, 16, 18. What is the variance? (2022)

A. 4
B. 6
C. 8
D. 10

Solution

Mean = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.

Correct Answer: A — 4

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Q. The scores of a test are: 20, 30, 40, 50. Calculate the variance. (2020)

A. 100
B. 200
C. 300
D. 400

Solution

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 250.

Correct Answer: B — 200

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Q. The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)

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

Solution

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).

Correct Answer: B — 15

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Q. The scores of five students are: 20, 22, 24, 26, 28. Calculate the variance. (2020)

A. 8
B. 10
C. 12
D. 14

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.

Correct Answer: A — 8

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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)

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

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8. SD = √8 = 2.83 (approximately 3).

Correct Answer: A — 2

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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the variance? (2020)

A. 4
B. 6
C. 8
D. 10

Solution

Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.

Correct Answer: A — 4

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Q. The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)

A. 3
B. 5
C. 7
D. 10

Solution

Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.

Correct Answer: B — 5

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Q. The standard deviation of a data set is 5. What is the variance? (2023)

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

Solution

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Correct Answer: B — 25

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Q. The variance of a sample is calculated as 25. What is the standard deviation?

A. 5
B. 10
C. 15
D. 20

Solution

Standard Deviation = √Variance = √25 = 5.

Correct Answer: A — 5

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Q. Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the dice is 7?

A. 1/6
B. 1/12
C. 1/36
D. 1/3

Solution

Possible outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 6 * 6 = 36. Probability = 6/36 = 1/6.

Correct Answer: A — 1/6

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Q. What is the mean of the following data set: 4, 8, 6, 5, 3? (2021)

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

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.2, rounded down to 5.

Correct Answer: C — 6

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Q. What is the median of the following data set: 12, 15, 14, 10, 18? (2023)

A. 12
B. 14
C. 15
D. 18

Solution

First, arrange the data in ascending order: 10, 12, 14, 15, 18. The median is the middle value, which is 14.

Correct Answer: B — 14

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Q. What is the median of the following data set: 3, 7, 9, 5, 11?

A. 5
B. 7
C. 9
D. 11

Solution

First, arrange the data in ascending order: 3, 5, 7, 9, 11. The median is the middle value, which is 7.

Correct Answer: B — 7

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Q. What is the median of the following data set: 5, 3, 8, 6, 2, 4?

A. 4
B. 5
C. 5.5
D. 6

Solution

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

Correct Answer: C — 5.5

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Q. What is the median of the following data: 1, 2, 3, 4, 5, 6, 7, 8?

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 values: (4 + 5) / 2 = 4.5.

Correct Answer: B — 4.5

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Q. What is the median of the following numbers: 10, 20, 30, 40, 50, 60, 70? (2022)

A. 30
B. 40
C. 50
D. 60

Solution

The numbers are in order. The median is the 4th number, which is 40.

Correct Answer: B — 40

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Q. What is the median of the following numbers: 22, 18, 25, 30, 20? (2021)

A. 20
B. 22
C. 25
D. 30

Solution

Arranging the numbers: 18, 20, 22, 25, 30. The median is the middle number, which is 22.

Correct Answer: A — 20

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Q. What is the median of the following numbers: 8, 3, 5, 12, 7, 10? (2023)

A. 5
B. 7
C. 8
D. 10

Solution

Arrange the numbers: 3, 5, 7, 8, 10, 12. The median is the average of the 3rd and 4th numbers: (7 + 8) / 2 = 7.5.

Correct Answer: C — 8

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Q. What is the median of the following set of numbers: 3, 7, 5, 9, 1? (2021)

A. 3
B. 5
C. 7
D. 9

Solution

To find the median, first arrange the numbers in ascending order: 1, 3, 5, 7, 9. The median is the middle number, which is 5.

Correct Answer: B — 5

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Q. What is the median of the following set: 4, 1, 7, 3, 9, 2? (2022)

A. 3
B. 4
C. 5
D. 6

Solution

Arranging the numbers: 1, 2, 3, 4, 7, 9. The median is the average of the 3rd and 4th numbers: (3 + 4) / 2 = 3.5.

Correct Answer: A — 3

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Q. What is the mode of the following data set: 2, 3, 4, 2, 5, 2, 3? (2023)

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

Solution

Mode is the number that appears most frequently. Here, 2 appears 3 times.

Correct Answer: A — 2

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Q. What is the mode of the following data set: 2, 3, 4, 4, 5, 5, 5, 6? (2023)

A. 4
B. 5
C. 6
D. 3

Solution

Mode is the number that appears most frequently. Here, 5 appears 3 times.

Correct Answer: B — 5

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Q. What is the mode of the following data set: 3, 7, 3, 2, 5, 3, 8? (2023)

A. 2
B. 3
C. 5
D. 7

Solution

The mode is the number that appears most frequently. Here, 3 appears 3 times, which is more than any other number.

Correct Answer: B — 3

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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 2? (2023)

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

Solution

The number 4 appears most frequently (3 times). Hence, mode = 4.

Correct Answer: D — 4

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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 5? (2019)

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

Solution

The mode is the number that appears most frequently. Here, 4 appears 3 times, so the mode is 4.

Correct Answer: C — 4

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

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

Solution

Mode is the number that appears most frequently. Here, 5 appears four times.

Correct Answer: A — 5

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

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

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

Solution

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

Correct Answer: D — 4

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

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

Solution

The mode is 5, as it appears 3 times, which is more than any other number.

Correct Answer: D — 5

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Statistics & Probability

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