Statistics & Probability for Competitive Exam Success

Statistics & Probability

Data Collection and Representation Data Collection and Representation - Applications Data Collection and Representation - Case Studies Data Collection and Representation - Problem Set Measures of Central Tendency (Mean, Median, Mode) Measures of Central Tendency (Mean, Median, Mode) - Applications Measures of Central Tendency (Mean, Median, Mode) - Case Studies Permutations and Combinations Basics Probability - Basic Concepts

Q. For the data set 1, 2, 3, 4, 5, what is the median?

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

Solution

Median is the middle value. The sorted data is 1, 2, 3, 4, 5. Median = 3.

Correct Answer: B — 3

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

A. 20
B. 30
C. 25
D. 40

Solution

Median = (30 + 40) / 2 = 35, since there are 5 numbers.

Correct Answer: B — 30

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Q. For the data set 12, 15, 12, 18, 20, what is the median?

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

Solution

Median = 15, as the sorted data is 12, 12, 15, 18, 20.

Correct Answer: A — 15

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Q. For the data set 3, 7, 8, 12, what is the median?

A. 7
B. 8
C. 10
D. 12

Solution

Median is the average of 7 and 8, which is 7.5.

Correct Answer: B — 8

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Q. For the dataset: 12, 15, 20, 22, 25, what is the median?

A. 15
B. 20
C. 22
D. 25

Solution

To find the median, arrange the numbers: 12, 15, 20, 22, 25. The median is the middle value, which is 20.

Correct Answer: B — 20

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Q. For the dataset: 4, 8, 6, 5, 3, what is the median?

A. 4
B. 5
C. 6
D. 8

Solution

First, arrange the numbers in ascending order: 3, 4, 5, 6, 8. The median is the middle value, which is 5.

Correct Answer: B — 5

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Q. For the following set of numbers: 5, 7, 9, 11, 13, what is the median?

A. 7
B. 9
C. 11
D. 13

Solution

The median is the middle value, which is 9.

Correct Answer: B — 9

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Q. For the numbers: 3, 3, 4, 5, 5, 5, 6, what is the mean?

A. 4
B. 5
C. 5.5
D. 6

Solution

Mean = (3 + 3 + 4 + 5 + 5 + 5 + 6) / 7 = 31 / 7 ≈ 4.43.

Correct Answer: B — 5

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Q. Given the following set of numbers: 3, 7, 7, 2, 5, what is the mode?

A. 2
B. 3
C. 5
D. 7

Solution

The mode is the number that appears most frequently. Here, 7 appears twice, which is more than any other number.

Correct Answer: D — 7

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Q. Given the numbers: 5, 7, 7, 8, 10, what is the mode?

A. 5
B. 7
C. 8
D. 10

Solution

The mode is the number that appears most frequently. Here, 7 appears twice.

Correct Answer: B — 7

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Q. How many different ways can you arrange 5 different colored balls in a row?

A. 60
B. 120
C. 240
D. 720

Solution

The number of arrangements of 5 balls is 5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: D — 720

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Q. How many different ways can you arrange the letters in the word 'MATH'?

A. 12
B. 16
C. 24
D. 36

Solution

The number of arrangements of 4 letters is 4! = 4 × 3 × 2 × 1 = 24.

Correct Answer: C — 24

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Q. How many different ways can you arrange the letters in the word 'SCHOOL'?

A. 120
B. 360
C. 720
D. 840

Solution

The number of arrangements of the letters in 'SCHOOL' is 6! / 2! = 360.

Correct Answer: B — 360

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Q. How many different ways can you choose 4 toppings from a selection of 10?

A. 210
B. 120
C. 100
D. 90

Solution

The number of combinations of 10 toppings taken 4 at a time is C(10, 4) = 210.

Correct Answer: A — 210

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Q. How many ways can you arrange 3 books on a shelf?

A. 3
B. 6
C. 9
D. 12

Solution

The number of arrangements of 3 books is 3! = 3 × 2 × 1 = 6.

Correct Answer: B — 6

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Q. How many ways can you arrange 5 books on a shelf?

A. 120
B. 60
C. 24
D. 30

Solution

The number of arrangements of 5 books is 5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

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Q. How many ways can you arrange the letters in the word 'BOOK'?

A. 12
B. 24
C. 16
D. 8

Solution

The number of arrangements is 4! / 2! = 12, since 'O' repeats.

Correct Answer: C — 16

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Q. How many ways can you choose 2 items from a set of 5?

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

Solution

C(5,2) = 5! / (2!(5-2)!) = 10.

Correct Answer: B — 10

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Q. How many ways can you choose 3 items from a set of 10?

A. 120
B. 720
C. 10
D. 100

Solution

The number of combinations is calculated as 10! / (3!(10-3)!) = 120.

Correct Answer: A — 120

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Q. How many ways can you choose 3 items from a set of 5 items?

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

Solution

C(5,3) = 5! / (3!(5-3)!) = 10

Correct Answer: A — 10

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Q. How many ways can you choose 3 items from a set of 5?

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

Solution

The number of ways to choose 3 items from 5 is calculated using combinations: C(5,3) = 5! / (3!(5-3)!) = 10.

Correct Answer: A — 10

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Q. How many ways can you choose 3 students from a group of 10?

A. 120
B. 210
C. 100
D. 30

Solution

The number of combinations is calculated as 10C3 = 10! / (3!(10-3)!) = 120.

Correct Answer: B — 210

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Q. How many ways can you select 1 card from a standard deck of 52 cards?

A. 1
B. 52
C. 104
D. 208

Solution

The number of ways to select 1 card from 52 is simply 52.

Correct Answer: B — 52

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Q. How many ways can you select 2 students from a class of 8?

A. 28
B. 56
C. 8
D. 14

Solution

The number of combinations of 8 students taken 2 at a time is C(8, 2) = 8! / (2!(8-2)!) = 28.

Correct Answer: A — 28

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Q. How many ways can you select 3 students from a group of 8?

A. 56
B. 84
C. 112
D. 128

Solution

The number of combinations of 3 students from 8 is C(8, 3) = 8! / (3!(8-3)!) = 56.

Correct Answer: B — 84

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Q. If a data set has a mean of 10 and a standard deviation of 2, what is the z-score of a value 12?

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

Solution

Z-score = (X - mean) / standard deviation = (12 - 10) / 2 = 1.

Correct Answer: A — 1

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Q. If a fair six-sided die is rolled, what is the probability of rolling a number greater than 4?

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

Solution

Numbers greater than 4 are 5 and 6. Probability = 2/6 = 1/3.

Correct Answer: B — 1/3

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Q. If the ages of a group of friends are: 22, 24, 26, 28, 30, what is the mean age?

A. 24
B. 26
C. 28
D. 30

Solution

Mean = (22 + 24 + 26 + 28 + 30) / 5 = 130 / 5 = 26.

Correct Answer: B — 26

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

A. 30
B. 25
C. 40
D. 35

Solution

Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30

Correct Answer: A — 30

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Q. If the data set is: 10, 20, 30, 40, 50, what is the variance?

A. 100
B. 200
C. 250
D. 300

Solution

Mean = 30; Variance = [(10-30)² + (20-30)² + (30-30)² + (40-30)² + (50-30)²] / 5 = 200.

Correct Answer: C — 250

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Statistics & Probability

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