Statistics & Probability for Competitive Exam Success

Statistics & Probability

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

Q. Calculate the range of the data set: 12, 15, 22, 30, 5.

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

Solution

Range = Maximum - Minimum = 30 - 5 = 25.

Correct Answer: A — 25

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Q. Calculate the range of the data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

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Q. Calculate the range of the data set: 8, 12, 15, 20, 22.

A. 10
B. 12
C. 14
D. 15

Solution

Range = Max - Min = 22 - 8 = 14.

Correct Answer: A — 10

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Q. Calculate the range of the following data set: 12, 15, 20, 22, 30.

A. 10
B. 12
C. 18
D. 20

Solution

Range = Maximum - Minimum = 30 - 12 = 18.

Correct Answer: C — 18

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Q. Calculate the range of the following data set: 15, 22, 8, 19, 30.

A. 7
B. 15
C. 22
D. 30

Solution

Range = max - min = 30 - 8 = 22.

Correct Answer: D — 30

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Q. Calculate the range of the following data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

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Q. Calculate the range of the following data set: 8, 12, 15, 7, 10.

A. 5
B. 8
C. 10
D. 12

Solution

Range = Maximum - Minimum = 15 - 7 = 8.

Correct Answer: A — 5

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Q. Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

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

Solution

Mean = 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: B — 6

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Q. Calculate the variance of the data set {4, 8, 6, 5, 3}.

A. 2.5
B. 3.2
C. 1.5
D. 4.0

Solution

Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.

Correct Answer: A — 2.5

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Q. Calculate the weighted mean of the following data: (10, 2), (20, 3), (30, 5).

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

Solution

Weighted Mean = (10*2 + 20*3 + 30*5) / (2 + 3 + 5) = 220 / 10 = 22.

Correct Answer: B — 25

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Q. Calculate the weighted mean of the following data: (2, 3), (4, 5), (6, 7) where the first number is the weight.

A. 4.5
B. 5
C. 5.5
D. 6

Solution

Weighted mean = (2*3 + 4*5 + 6*7) / (2 + 4 + 6) = (6 + 20 + 42) / 12 = 68 / 12 = 5.67.

Correct Answer: C — 5.5

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Q. Calculate the weighted mean of the numbers 10, 20, and 30 with weights 1, 2, and 3 respectively.

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

Solution

Weighted mean = (10*1 + 20*2 + 30*3) / (1 + 2 + 3) = 140 / 6 = 23.33.

Correct Answer: B — 25

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Q. Calculate 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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Q. Find the arithmetic mean of the first five prime numbers.

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

Solution

First five primes: 2, 3, 5, 7, 11. Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.

Correct Answer: C — 7

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Q. Find the arithmetic mean of the numbers 12, 15, 18, 21, and 24.

A. 18
B. 19
C. 20
D. 21

Solution

Mean = (12 + 15 + 18 + 21 + 24) / 5 = 90 / 5 = 18.

Correct Answer: A — 18

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Q. Find the median of the following numbers: 1, 3, 3, 6, 7, 8, 9.

A. 3
B. 6
C. 7
D. 8

Solution

Arranging the numbers: 1, 3, 3, 6, 7, 8, 9. Median = 6 (middle value).

Correct Answer: B — 6

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Q. Find the median of the following set of numbers: 1, 3, 3, 6, 7, 8, 9.

A. 3
B. 6
C. 7
D. 8

Solution

Arranging the numbers: 1, 3, 3, 6, 7, 8, 9. Median = 6 (middle value).

Correct Answer: B — 6

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Q. Find the median of the following set of numbers: 3, 1, 4, 2.

A. 2
B. 2.5
C. 3
D. 3.5

Solution

Arranging the numbers: 1, 2, 3, 4. Median = (2 + 3) / 2 = 2.5.

Correct Answer: B — 2.5

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Q. Find the range of the data set: 10, 15, 20, 25, 30.

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

Solution

Range = Maximum - Minimum = 30 - 10 = 20.

Correct Answer: A — 15

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Q. Find the range of the data set: 12, 15, 20, 22, 30.

A. 10
B. 15
C. 18
D. 20

Solution

Range = Maximum - Minimum = 30 - 12 = 18.

Correct Answer: C — 18

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Q. Find the range of the data set: 12, 15, 22, 30, 5.

A. 25
B. 22
C. 30
D. 15

Solution

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

Correct Answer: A — 25

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Q. Find the range of the data set: 8, 12, 15, 20, 25.

A. 12
B. 15
C. 17
D. 20

Solution

Range = Maximum - Minimum = 25 - 8 = 17.

Correct Answer: A — 12

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Q. Find the weighted mean of the numbers 10, 20, and 30 with weights 1, 2, and 3 respectively.

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

Solution

Weighted mean = (10*1 + 20*2 + 30*3) / (1 + 2 + 3) = (10 + 40 + 90) / 6 = 140 / 6 = 23.33.

Correct Answer: B — 25

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Q. For the data set 10, 20, 30, 40, 50, what is the mean deviation?

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

Solution

Mean = 30; Mean Deviation = (|10-30| + |20-30| + |30-30| + |40-30| + |50-30|) / 5 = 10.

Correct Answer: B — 15

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Q. For the data set {10, 12, 23, 23, 16, 23, 21}, what is the mode?

A. 10
B. 12
C. 23
D. 21

Solution

The mode is the number that appears most frequently, which is 23.

Correct Answer: C — 23

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Q. For the data set {12, 15, 20, 22, 25}, what is the mode?

A. 12
B. 15
C. 20
D. No mode

Solution

There is no mode as all values appear only once.

Correct Answer: D — No mode

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Q. For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

A. 2
B. 1.6
C. 3
D. 2.5

Solution

Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.

Correct Answer: B — 1.6

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Q. For the data set {4, 8, 6, 5, 3}, what is the mean?

A. 4.5
B. 5.5
C. 6.0
D. 5.0

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.0.

Correct Answer: D — 5.0

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Q. For the data set: 1, 2, 3, 4, 5, what is the interquartile range?

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

Solution

Q1 = 2, Q3 = 4; Interquartile Range = Q3 - Q1 = 4 - 2 = 2.

Correct Answer: B — 2

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Q. For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

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

Solution

Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.

Correct Answer: B — 2

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Statistics & Probability

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