Q. If the mean of a data set is 20 and the standard deviation is 4, what is the coefficient of variation?
A.
20%
B.
25%
C.
15%
D.
10%
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Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4 / 20) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If the mean of a data set is 50 and the standard deviation is 10, what is the coefficient of variation?
A.
20%
B.
10%
C.
15%
D.
25%
Show solution
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (10 / 50) * 100 = 20%.
Correct Answer:
A
— 20%
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Q. If the range of a data set is 15 and the minimum value is 5, what is the maximum value?
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Solution
Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 15 + 5 = 20.
Correct Answer:
C
— 20
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Q. If the standard deviation of a data set is 0, what can be said about the data?
A.
All values are different
B.
All values are the same
C.
Values are in a range
D.
Data is not valid
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Solution
A standard deviation of 0 indicates that all values in the data set are the same.
Correct Answer:
B
— All values are the same
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Q. If the standard deviation of a data set is 3, what is the variance?
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Solution
Variance = (Standard Deviation)^2 = 3^2 = 9.
Correct Answer:
C
— 9
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetrical
D.
Uniform
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Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer:
A
— Skewed right
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred?
A.
Data is skewed right
B.
Data is skewed left
C.
Data is symmetric
D.
Data is uniform
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Solution
Since the mean is greater than the median, the data is skewed to the right.
Correct Answer:
A
— Data is skewed right
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Q. In a data set, if the mean is 50 and the median is 45, what can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetric
D.
Uniform
Show solution
Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer:
A
— Skewed right
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Q. In a data set, if the mode is 15 and the mean is 20, what can be said about the data?
A.
Positively skewed
B.
Negatively skewed
C.
Symmetrical
D.
Uniform
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Solution
Since the mean is greater than the mode, the data is positively skewed.
Correct Answer:
A
— Positively skewed
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Q. In a data set, the mean is 10 and the standard deviation is 2. What is the coefficient of variation?
A.
20%
B.
10%
C.
5%
D.
15%
Show solution
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (2/10) * 100 = 20%.
Correct Answer:
A
— 20%
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Q. In a data set, the mean is 20 and the median is 18. What can be inferred about the data?
A.
Skewed right
B.
Skewed left
C.
Symmetric
D.
Uniform
Show solution
Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer:
A
— Skewed right
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Q. In a data set, the mean is 20 and the median is 18. What can be said about the data?
A.
Positively skewed
B.
Negatively skewed
C.
Symmetrical
D.
Uniform
Show solution
Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer:
A
— Positively skewed
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Q. In a data set, the mean is 20 and the standard deviation is 4. What is the coefficient of variation?
A.
20%
B.
15%
C.
10%
D.
5%
Show solution
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4/20) * 100 = 20%.
Correct Answer:
A
— 20%
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Q. In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
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Solution
Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Correct Answer:
B
— 2
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Q. In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?
A.
50%
B.
68%
C.
75%
D.
95%
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Solution
In a normal distribution, approximately 68% of the data lies within one standard deviation of the mean.
Correct Answer:
B
— 68%
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Q. In a normal distribution, what percentage of data lies within one standard deviation of the mean?
A.
50%
B.
68%
C.
75%
D.
95%
Show solution
Solution
In a normal distribution, approximately 68% of the data lies within one standard deviation of the mean.
Correct Answer:
B
— 68%
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Q. The interquartile range of the data set: 1, 2, 3, 4, 5, 6, 7, 8 is:
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Solution
Q1 = 3, Q3 = 6. Interquartile Range = Q3 - Q1 = 6 - 3 = 3.
Correct Answer:
B
— 3
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Q. The mean of a data set is 50 and the standard deviation is 5. What is the coefficient of variation?
A.
5%
B.
10%
C.
15%
D.
20%
Show solution
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.
Correct Answer:
B
— 10%
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Q. The range of the data set 1, 3, 5, 7, 9 is:
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Solution
Range = Maximum - Minimum = 9 - 1 = 8.
Correct Answer:
A
— 8
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Q. The range of the data set {10, 15, 20, 25, 30} is?
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Solution
Range = Maximum value - Minimum value = 30 - 10 = 20.
Correct Answer:
A
— 15
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Q. What is the 75th percentile of the data set {10, 20, 30, 40, 50}?
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Solution
The 75th percentile (Q3) is the value below which 75% of the data falls, which is 40.
Correct Answer:
A
— 40
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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 10?
A.
20%
B.
10%
C.
15%
D.
25%
Show solution
Solution
Coefficient of variation = (Standard deviation / Mean) * 100 = (10 / 50) * 100 = 20%.
Correct Answer:
A
— 20%
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Q. What is the coefficient of variation if the mean is 50 and the standard deviation is 5?
A.
5%
B.
10%
C.
15%
D.
20%
Show solution
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.
Correct Answer:
B
— 10%
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Q. What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?
Show solution
Solution
Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.
Correct Answer:
B
— 6
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
Show solution
Solution
IQR = Q3 - Q1; Q1 = 3, Q3 = 8; IQR = 8 - 3 = 5.
Correct Answer:
A
— 5
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?
Show solution
Solution
Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.
Correct Answer:
A
— 6
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Q. What is the interquartile range (IQR) of the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9?
Show solution
Solution
Q1 = 3, Q3 = 7; IQR = Q3 - Q1 = 7 - 3 = 4.
Correct Answer:
A
— 4
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Q. What is the interquartile range (IQR) of the data set: 1, 3, 5, 7, 9, 11, 13?
Show solution
Solution
Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.
Correct Answer:
B
— 6
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Q. What is the median of the data set {7, 3, 5, 9, 1}?
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Solution
First, arrange the data: {1, 3, 5, 7, 9}. The median is the middle value, which is 5.
Correct Answer:
A
— 5
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Q. What is the mode of the data set: 1, 2, 2, 3, 4, 4, 4, 5?
Show solution
Solution
The mode is the number that appears most frequently, which is 4.
Correct Answer:
D
— 4
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Showing 31 to 60 of 75 (3 Pages)
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.
