Statistics & Probability for Competitive Exam Success

Statistics & Probability

Mean Median Mode Probability Rules Variance & SD

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

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. 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. For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

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

Solution

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

Correct Answer: A — 8

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Q. For the data set: 10, 12, 14, 16, what is the variance? (2019)

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.

Correct Answer: B — 4

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Q. For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

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

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6. Variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²] / 5 = 8.

Correct Answer: A — 6

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Q. For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)

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

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

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Q. For the data set: 5, 7, 9, 11, 13, what is the variance?

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

Solution

Mean = 9. Variance = [(5-9)² + (7-9)² + (9-9)² + (11-9)² + (13-9)²] / 5 = 8.

Correct Answer: A — 4

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Q. For the data set: 5, 8, 12, 15, 20, what is the median? (2020)

A. 12
B. 15
C. 10
D. 8

Solution

Arranging the numbers: 5, 8, 12, 15, 20. The median is the middle number, which is 12.

Correct Answer: A — 12

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Q. For the data set: 6, 7, 8, 8, 9, 9, 9, 10, what is the mode?

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

Solution

The mode is 9, as it appears most frequently (three times) in the data set.

Correct Answer: D — 9

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Q. Given the data set 8, 8, 9, 10, 10, 10, 11, 12, what is the mode?

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

Solution

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

Correct Answer: C — 10

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Q. Given the data set: 1, 1, 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 three times, more than any other number.

Correct Answer: C — 4

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Q. If a die is rolled, what is the probability of rolling an even number?

A. 1/2
B. 1/3
C. 1/6
D. 2/3

Solution

Even numbers on a die are 2, 4, 6. Total outcomes = 6. Probability = Number of even outcomes / Total outcomes = 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. If a student is selected at random from a group of 15 students, where 9 are girls and 6 are boys, what is the probability that the selected student is a boy? (2021)

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

Solution

Probability of selecting a boy = Number of boys / Total students = 6/15 = 2/5.

Correct Answer: B — 2/5

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Q. If a student is selected at random from a group of 15 students, where 9 are girls and 6 are boys, what is the probability that the student is a boy? (2023)

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

Solution

Probability of selecting a boy = Number of boys / Total students = 6/15 = 2/5.

Correct Answer: B — 1/3

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Q. If a student is selected at random from a group of 40 students, where 25 are girls and 15 are boys, what is the probability that the selected student is a boy?

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

Solution

Probability of selecting a boy = Number of boys / Total students = 15/40 = 3/8.

Correct Answer: A — 3/8

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Q. If the average of 10 numbers is 50, what is the sum of these numbers?

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

Solution

Sum = Average * Number of items = 50 * 10 = 500.

Correct Answer: A — 500

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Q. If the average of 6 numbers is 30, what is the average if one number is increased by 10?

A. 30
B. 32
C. 34
D. 36

Solution

Total of 6 numbers = 6 * 30 = 180.\n\nNew total = 180 + 10 = 190.\n\nNew average = 190 / 6 = 31.67.

Correct Answer: B — 32

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Q. If the average of 7, 9, 11, and 13 is x, what is the value of x? (2023)

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

Solution

Mean = (7 + 9 + 11 + 13) / 4 = 10.

Correct Answer: B — 10

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Q. If the average of a set of numbers is 12 and there are 6 numbers, what is the total sum of the numbers?

A. 60
B. 72
C. 84
D. 96

Solution

Total sum = Average * Number of items = 12 * 6 = 72.

Correct Answer: B — 72

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Q. If the average of five numbers is 60, what is the total of these numbers?

A. 300
B. 250
C. 350
D. 400

Solution

The total of the five numbers is calculated as average * number of items = 60 * 5 = 300.

Correct Answer: A — 300

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Q. If the data set is 2, 4, 6, 8, 10, 12, what is the median? (2021)

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

Solution

The numbers are already in order. Since there are 6 numbers, the median is the average of the 3rd and 4th numbers: (6 + 8) / 2 = 7.

Correct Answer: C — 8

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Q. If the data set is 8, 8, 9, 10, 10, 10, 11, 12, what is the mode?

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

Solution

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

Correct Answer: C — 10

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Q. If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

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

Solution

Mean = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 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: C — 6

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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 data set is: 5, 7, 9, 11, what is the variance? (2022)

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

Solution

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

Correct Answer: A — 2

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Q. If the following numbers are given: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, what is the median? (2019)

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

Solution

The numbers are already in order. The median is the average of the 5th and 6th numbers: (5 + 6) / 2 = 5.5.

Correct Answer: B — 6

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Q. If the mean of 10 numbers is 50, what is the mean of the first 5 numbers if their sum is 200?

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

Solution

Mean of 10 numbers = 50, so total sum = 500. Sum of last 5 numbers = 500 - 200 = 300. Mean of last 5 = 300 / 5 = 60.

Correct Answer: D — 60

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Q. If the mean of 12 numbers is 25, what is the sum of these numbers?

A. 250
B. 300
C. 275
D. 225

Solution

The sum of the numbers is calculated as mean * number of items = 25 * 12 = 300.

Correct Answer: A — 250

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Q. If the mean of a data set is 10 and the number of observations is 5, what is the sum of the observations?

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

Solution

Sum = Mean * Number of observations = 10 * 5 = 50.

Correct Answer: A — 50

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Q. If the mean of a data set is 15 and the standard deviation is 5, what is the variance? (2022)

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

Solution

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

Correct Answer: D — 25

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Statistics & Probability

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