Measures of Dispersion for Competitive Exam Success

Measures of Dispersion

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 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: 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. Which measure of dispersion is affected by extreme values?

A. Range
B. Variance
C. Standard Deviation
D. All of the above

Solution

All of these measures are affected by extreme values in the data set.

Correct Answer: D — All of the above

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Q. Which measure of dispersion is not affected by extreme values?

A. Range
B. Variance
C. Standard Deviation
D. Interquartile Range

Solution

Interquartile Range is not affected by extreme values.

Correct Answer: D — Interquartile Range

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Q. Which of the following measures is NOT a measure of dispersion?

A. Range
B. Variance
C. Mean
D. Standard Deviation

Solution

Mean is a measure of central tendency, not dispersion.

Correct Answer: C — Mean

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Q. Which of the following measures of dispersion is affected by extreme values?

A. Range
B. Interquartile Range
C. Variance
D. Standard Deviation

Solution

Range is affected by extreme values as it is calculated as the difference between the maximum and minimum values.

Correct Answer: A — Range

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Measures of Dispersion MCQ & Objective Questions

Understanding Measures of Dispersion is crucial for students aiming to excel in their exams. This topic not only helps in grasping the spread of data but also plays a significant role in scoring well in objective questions. Practicing MCQs related to Measures of Dispersion can enhance your exam preparation and boost your confidence in tackling important questions effectively.

What You Will Practise Here

Definitions and significance of Measures of Dispersion
Key concepts: Range, Variance, Standard Deviation, and Interquartile Range
Formulas for calculating different measures of dispersion
Real-life applications of Measures of Dispersion
Diagrams illustrating data spread and distribution
Comparison of different measures of dispersion
Sample and population measures of dispersion

Exam Relevance

Measures of Dispersion is a vital topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of the concepts, calculations, and applications of these measures. Common question patterns include direct calculations, interpretation of data sets, and application-based scenarios, making it essential to master this topic for better performance.

Common Mistakes Students Make

Confusing between population and sample measures of dispersion
Miscalculating variance and standard deviation due to incorrect formula application
Overlooking the significance of outliers in data sets
Failing to interpret the results of dispersion measures correctly

FAQs

Question: What is the primary purpose of Measures of Dispersion?
Answer: Measures of Dispersion help in understanding the variability or spread of a data set, which is essential for data analysis.

Question: How do I calculate the standard deviation?
Answer: The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

Now that you have a clear understanding of Measures of Dispersion, it's time to put your knowledge to the test! Solve practice MCQs and enhance your understanding to excel in your exams.

Measures of Dispersion

Measures of Dispersion MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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