Statistics & Probability for Competitive Exam Success

Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

Q. If the mean of a set of numbers is 25 and there are 8 numbers, what is the total of these numbers? (2022)

A. 150
B. 200
C. 250
D. 300

Solution

Total = Mean * Number of Items = 25 * 8 = 200.

Correct Answer: C — 250

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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 five numbers is 20, what is their total sum? (2020)

A. 80
B. 100
C. 120
D. 140

Solution

Mean = Total Sum / Number of Items. Therefore, Total Sum = Mean * Number of Items = 20 * 5 = 100.

Correct Answer: A — 80

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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 mean of the first n natural numbers is 10, what is the value of n?

A. 20
B. 19
C. 18
D. 15

Solution

Mean = n(n + 1) / (2n) = 10.\n\n(n + 1) / 2 = 10\n\n(n + 1) = 20\n\nn = 19.

Correct Answer: A — 20

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Q. If the mean of the following data set is 20: 15, 18, 22, x, 25, what is the value of x? (2019)

A. 20
B. 22
C. 24
D. 26

Solution

Mean = (15 + 18 + 22 + x + 25) / 5 = 20. Solving gives x = 24.

Correct Answer: C — 24

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Q. If the median of the data set 3, 7, 5, 9, 11 is x, what is the value of x? (2022)

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

Solution

Arranging the data: 3, 5, 7, 9, 11. Median = 7.

Correct Answer: B — 7

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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 numbers 8, 3, 5, 12, and 7 are given, what is the median? (2022)

A. 5
B. 7
C. 8
D. 12

Solution

Arranging the numbers: 3, 5, 7, 8, 12. The median is the middle number, which is 7.

Correct Answer: B — 7

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Q. If the probability of an event A is 0.4, what is the probability of the event not occurring? (2021)

A. 0.4
B. 0.6
C. 0.8
D. 0.2

Solution

Probability of not A = 1 - P(A) = 1 - 0.4 = 0.6.

Correct Answer: B — 0.6

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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 range of a data set is 20 and the minimum value is 10, what is the maximum value? (2023)

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

Solution

Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 20 + 10 = 30.

Correct Answer: A — 30

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Q. If the range of a data set is 20 and the minimum value is 5, what is the maximum value? (2023)

A. 15
B. 20
C. 25
D. 30

Solution

Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 20 + 5 = 25.

Correct Answer: C — 25

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Q. If the variance of a data set is 16, what is the range of the data if the minimum value is 0? (2023)

A. 8
B. 16
C. 4
D. 12

Solution

Standard deviation = √16 = 4. If the minimum is 0, the maximum can be 4, thus range = 4 - 0 = 4.

Correct Answer: A — 8

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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 population is 25, what is the standard deviation? (2022)

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

Solution

Standard deviation = √25 = 5.

Correct Answer: A — 5

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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 15 students, their ages are: 14, 15, 16, 14, 15, 16, 17, 18, 19, 20, 14, 15, 16, 17, 18. What is the median age? (2023)

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

Solution

Arranging the ages: 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 20. The median is the 8th number, which is 16.

Correct Answer: B — 16

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Q. In a class of 30 students, 18 are boys and 12 are girls. If one student is selected at random, what is the probability that the student is a girl?

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

Solution

Probability = Number of girls / Total students = 12/30 = 2/5.

Correct Answer: A — 2/5

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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 class of 5 students, their ages are 16, 18, 17, 19, and 20. What is the median age? (2022)

A. 17
B. 18
C. 19
D. 20

Solution

Arrange the ages: 16, 17, 18, 19, 20. The median is the middle value, which is 18.

Correct Answer: B — 18

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Q. In a class, the marks obtained by students are: 45, 55, 45, 60, 70, 55, 55. What is the mode of the marks?

A. 45
B. 55
C. 60
D. 70

Solution

The mode is 55, as it appears three times in the data set.

Correct Answer: B — 55

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Q. In a class, the number of pets owned by students is recorded as follows: 0, 1, 2, 1, 3, 1, 2. What is the mode?

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

Solution

The mode is 1, which appears 3 times in the data set.

Correct Answer: B — 1

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Q. In a class, the number of students who scored the following grades: A, A, B, B, B, C, C, D. What is the mode?

A. A
B. B
C. C
D. D

Solution

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

Correct Answer: B — B

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Q. In a data set of 10 numbers, if the numbers are arranged in ascending order, what is the median? (2020)

A. Average of 5th and 6th
B. 5th number
C. 6th number
D. Average of 1st and 10th

Solution

For an even number of observations, the median is the average of the two middle numbers, which are the 5th and 6th numbers.

Correct Answer: A — Average of 5th and 6th

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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 10 numbers, the numbers are: 2, 3, 4, 4, 5, 5, 5, 6, 7, 8. What is the mode of this data set?

A. 2
B. 4
C. 5
D. 6

Solution

The mode is the number that appears most frequently. Here, 5 appears 3 times, which is more than any other number.

Correct Answer: C — 5

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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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Statistics & Probability

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