Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/5

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Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?

A. 1/10
B. 1/5
C. 1/2
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: B — 1/5

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Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of red = 5/8.

Correct Answer: B — 5/8

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Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)

A. 76
B. 77
C. 78
D. 79

Solution

Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.

Correct Answer: B — 77

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Q. A coin is tossed three times. What is the probability of getting at least one head?

A. 1/8
B. 1/2
C. 7/8
D. 3/8

Solution

Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.

Correct Answer: C — 7/8

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Q. A data set has values: 10, 12, 14, 16. What is the variance? (2021)

A. 2
B. 4
C. 6
D. 8

Solution

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.

Correct Answer: B — 4

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Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. If one marble is drawn, what is the probability that it is either red or yellow?

A. 1/2
B. 2/5
C. 4/10
D. 7/10

Solution

Total marbles = 5 + 3 + 2 = 10. Probability of red or yellow = (Number of red + Number of yellow) / Total = (5 + 2) / 10 = 7/10.

Correct Answer: D — 7/10

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Q. A set of numbers has a mean of 20. If one number is removed, the mean becomes 18. What was the number removed? (2022)

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

Solution

Let the number of elements be n. Then, 20n - x = 18(n - 1). Solving gives x = 22.

Correct Answer: A — 22

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Q. A set of numbers has the following frequencies: 10 (1), 20 (2), 30 (3), 40 (4). What is the mode of this set? (2021)

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

Solution

The number 40 appears most frequently (4 times), so the mode is 40.

Correct Answer: D — 40

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Q. A survey of favorite fruits among 20 people resulted in the following counts: Apple (6), Banana (8), Orange (4), Grape (2). What is the mode of the favorite fruits? (2023)

A. Apple
B. Banana
C. Orange
D. Grape

Solution

Banana has the highest count (8), so the mode is Banana.

Correct Answer: B — Banana

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Q. For the data set: 1, 2, 3, 4, 5, what is the variance? (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. If the data set is: 5, 5, 5, 5, what is the variance? (2019)

A. 0
B. 1
C. 2
D. 5

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. If the mean of a dataset is 50 and there are 10 numbers, what is the total sum of the numbers? (2021)

A. 500
B. 600
C. 550
D. 450

Solution

Total sum = Mean * Number of elements = 50 * 10 = 500.

Correct Answer: A — 500

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Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)

A. 180
B. 150
C. 120
D. 200

Solution

Total sum = Mean * Number of elements = 30 * 6 = 180.

Correct Answer: A — 180

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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)

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

Solution

Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.

Correct Answer: A — 30

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Q. If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)

A. 8
B. 9
C. 10
D. 11

Solution

For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.

Correct Answer: A — 8

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Q. If the mode of the following numbers: 3, 3, 4, 5, 5, 5, 6, 7 is removed, what will be the new mode? (2019)

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

Solution

Removing 5, which is the mode, leaves 3 as the new mode since it appears twice.

Correct Answer: A — 3

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Q. If the mode of the following set of numbers: 1, 2, 2, 3, 4, 4, 4, 5 is increased by 1, what will be the new mode? (2022)

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

Solution

The original mode is 4. Increasing it by 1 gives a new mode of 5.

Correct Answer: C — 4

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Q. If the probability of an event occurring is 0.3, what is the probability of it not occurring? (2023)

A. 0.3
B. 0.7
C. 0.5
D. 0.1

Solution

Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.

Correct Answer: B — 0.7

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Q. If the variance of a population is 16, what is the standard deviation? (2023)

A. 4
B. 8
C. 16
D. 2

Solution

Standard deviation is the square root of variance. Therefore, SD = √16 = 4.

Correct Answer: A — 4

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Q. If the variance of a sample is 25, what is the standard deviation? (2023)

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

Solution

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Correct Answer: A — 5

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Q. In a class of 30 students, the marks obtained are as follows: 45, 50, 50, 55, 60, 60, 60, 70, 75. What is the mode of the marks? (2019)

A. 50
B. 60
C. 70
D. 75

Solution

The number 60 appears most frequently (3 times), so the mode is 60.

Correct Answer: B — 60

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Q. In a data set of 10 numbers, the mode is 5. If the number 5 is replaced by 7, what will be the new mode? (2021)

A. 5
B. 7
C. No mode
D. Cannot be determined

Solution

Replacing 5 with 7 removes the most frequent number, so the new mode is 7.

Correct Answer: B — 7

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Q. In a data set of 12 values: 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, what is the mode? (2023)

A. 1
B. 2
C. 5
D. No mode

Solution

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

Correct Answer: C — 5

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Q. In a frequency distribution, the following data is given: 1 (2 times), 2 (3 times), 3 (3 times), 4 (1 time). What is the mode? (2020)

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

Solution

Both 2 and 3 appear 3 times, but since 2 is the smallest, the mode is 2.

Correct Answer: B — 2

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Q. In a group of 15 people, the ages are: 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29. What is the mode of the ages? (2022)

A. 21
B. 22
C. 25
D. 26

Solution

The age 22 appears 3 times, which is more than any other age, so the mode is 22.

Correct Answer: C — 25

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Q. In a lottery, the probability of winning is 0.2. What is the probability of losing?

A. 0.2
B. 0.5
C. 0.8
D. 0.1

Solution

Probability of losing = 1 - P(winning) = 1 - 0.2 = 0.8.

Correct Answer: C — 0.8

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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. 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 mean of 5, 15, 25, and x is 20. Find the value of x. (2023)

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

Solution

Mean = (5 + 15 + 25 + x) / 4 = 20. Solving gives x = 30.

Correct Answer: C — 30

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Statistics & Probability

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