Statistics & Probability for Competitive Exam Success

Statistics & Probability

Bayes Theorem Conditional Probability Measures of Central Tendency Measures of Dispersion Probability Basics

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

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

Solution

Mode = 3 (most frequent value).

Correct Answer: C — 3

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

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

Solution

The mode is 4 as it appears most frequently (3 times).

Correct Answer: C — 4

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

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

Solution

Mode is the number that appears most frequently. Here, mode = 2.

Correct Answer: B — 2

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Q. What is the mode of the following data set: {1, 1, 2, 2, 3, 3, 3, 4}?

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

Solution

Mode is 3 as it appears most frequently (3 times).

Correct Answer: C — 3

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Q. What is the probability of drawing a red card from a standard deck of cards?

A. 1/2
B. 1/4
C. 1/3
D. 1/6

Solution

There are 26 red cards in a deck of 52. Probability = 26/52 = 1/2.

Correct Answer: A — 1/2

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Q. What is the probability of drawing an ace from a standard deck of cards?

A. 1/52
B. 1/13
C. 1/26
D. 1/4

Solution

There are 4 aces in a deck of 52 cards. Therefore, the probability P(ace) = 4/52 = 1/13.

Correct Answer: B — 1/13

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Q. What is the probability of getting a sum of 7 when two dice are rolled?

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

Solution

The possible outcomes for a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) which gives us 6 favorable outcomes. Total outcomes when rolling two dice = 6 * 6 = 36. Therefore, P(sum of 7) = 6/36 = 1/6.

Correct Answer: A — 1/6

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Q. What is the probability of rolling an even number on a fair six-sided die?

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

Solution

Even numbers on a die: 2, 4, 6. Probability = 3/6 = 1/2.

Correct Answer: C — 1/2

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Q. What is the probability of rolling an even number on a single die?

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

Solution

Even numbers on a die = 2, 4, 6. Probability = 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. What is the probability of rolling an even number on a single six-sided die?

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

Solution

The even numbers on a die are 2, 4, and 6. There are 3 even numbers out of 6 total numbers, so the probability is 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. What is the probability of selecting a vowel from the English alphabet?

A. 1/5
B. 1/10
C. 1/26
D. 1/13

Solution

There are 5 vowels (A, E, I, O, U) in the English alphabet of 26 letters. Therefore, P(vowel) = 5/26.

Correct Answer: A — 1/5

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Q. What is the range of the data set {15, 22, 18, 30, 25}?

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

Solution

Range = Maximum value - Minimum value = 30 - 15 = 15.

Correct Answer: A — 15

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Q. What is the range of the data set {15, 22, 30, 18, 25}?

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

Solution

Range = Maximum - Minimum = 30 - 15 = 15.

Correct Answer: A — 15

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Q. What is the range of the data set {4, 8, 6, 5, 3}?

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

Solution

Range = Maximum value - Minimum value = 8 - 3 = 5.

Correct Answer: A — 5

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Q. What is the range of the data set {5, 8, 12, 15, 20}?

A. 15
B. 12
C. 10
D. 5

Solution

Range = Maximum value - Minimum value = 20 - 5 = 15.

Correct Answer: A — 15

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Q. What is the range of the data set: 12, 15, 22, 30, 5?

A. 25
B. 27
C. 22
D. 30

Solution

Range = max - min = 30 - 5 = 25.

Correct Answer: A — 25

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Q. What is the range of the data set: 5, 10, 15, 20, 25?

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

Solution

Range = Maximum - Minimum = 25 - 5 = 20.

Correct Answer: A — 15

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Q. What is the range of the data set: 5, 7, 9, 12, 15?

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

Solution

Range = Maximum - Minimum = 15 - 5 = 10.

Correct Answer: A — 10

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Q. What is the range of the following data set: 10, 20, 30, 40, 50?

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

Solution

Range = Maximum - Minimum = 50 - 10 = 40.

Correct Answer: A — 30

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Q. What is the range of the following data set: 5, 10, 15, 20, 25?

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

Solution

Range = Maximum - Minimum = 25 - 5 = 20.

Correct Answer: A — 15

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Q. What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?

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

Solution

Mean = 19.5, Variance = 25, Standard Deviation = √25 = 5.

Correct Answer: A — 5

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Q. What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?

A. 5.5
B. 4.5
C. 6.5
D. 3.5

Solution

Mean = 19.14, Variance = 20.25, Standard Deviation = √20.25 = 4.5.

Correct Answer: B — 4.5

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Q. What is the standard deviation of the data set {4, 8, 6, 5, 3}?

A. 1.58
B. 2.58
C. 3.58
D. 4.58

Solution

Mean = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 6.56. Standard Deviation = √6.56 ≈ 2.56.

Correct Answer: B — 2.58

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Q. What is the standard deviation of the data set: 1, 2, 3, 4, 5?

A. 1
B. 1.5
C. 2
D. 2.5

Solution

Mean = 3. Standard Deviation = sqrt[((1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2)/5] = sqrt[2] = 1.414.

Correct Answer: A — 1

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Q. What is the variance of the data set {4, 8, 6, 5, 3}?

A. 2.5
B. 3
C. 4
D. 5

Solution

Mean = 5.2; Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²] / 5 = 2.56.

Correct Answer: A — 2.5

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Q. What is the variance of the data set: 1, 2, 3, 4, 5?

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

Solution

Mean = 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. What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

A. 2.5
B. 3.5
C. 4.5
D. 5.5

Solution

Mean = 5.0; 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 = 2.5.

Correct Answer: A — 2.5

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Q. What is the variance of the following data set: {5, 7, 8, 9, 10}?

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

Solution

Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.

Correct Answer: B — 3

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Q. What is the weighted mean of the scores 70, 80, 90 with weights 1, 2, 3 respectively?

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Q. What is the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively?

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Statistics & Probability

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