Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.
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Solution
Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.
Correct Answer:
A
— 4
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Q. Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.
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Solution
Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.
Correct Answer:
B
— 1.5
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Q. Calculate the mean of the following data: 5, 10, 15, 20.
A.
10
B.
12.5
C.
15
D.
17.5
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Solution
Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.
Correct Answer:
B
— 12.5
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Q. Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.
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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
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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. Find the range of the data set: 10, 15, 20, 25, 30.
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Solution
Range = Maximum - Minimum = 30 - 10 = 20.
Correct Answer:
A
— 15
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Q. For the data set 10, 20, 30, 40, 50, what is the mean deviation?
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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?
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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
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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?
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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
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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?
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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. For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
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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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Q. For the data set: 5, 7, 8, 9, 10, what is the standard deviation?
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Solution
Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41
Correct Answer:
B
— 2
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Q. If the data set has a mean of 30 and a median of 25, what does this indicate?
A.
Data is symmetrical
B.
Data is positively skewed
C.
Data is negatively skewed
D.
Data is uniform
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Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer:
B
— Data is positively skewed
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.
Correct Answer:
C
— 2
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1
Correct Answer:
C
— 2
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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer:
A
— 4
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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?
A.
Symmetric
B.
Positively skewed
C.
Negatively skewed
D.
Uniform
Show solution
Solution
Since the mean is greater than the median, the distribution is positively skewed.
Correct Answer:
B
— Positively skewed
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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?
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Solution
Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.
Correct Answer:
B
— 2
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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer:
B
— 4
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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?
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Solution
Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.
Correct Answer:
B
— 3
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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?
A.
1.58
B.
2.58
C.
3.58
D.
4.58
Show solution
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 = 2.5. Standard Deviation = √2.5 ≈ 1.58.
Correct Answer:
A
— 1.58
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Q. If the data set is: 3, 7, 7, 19, what is the median?
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Solution
Median = (7 + 7) / 2 = 7.
Correct Answer:
A
— 7
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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?
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Solution
Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.
Correct Answer:
B
— 8
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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
Show solution
Solution
The standard deviation remains the same because the transformation is a shift.
Correct Answer:
C
— Remains the same
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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
Show solution
Solution
Standard deviation remains the same as adding a constant does not affect dispersion.
Correct Answer:
C
— Remains the same
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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?
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Solution
Q1 is the median of the first half of the data set {3, 7}, which is 7.
Correct Answer:
B
— 7
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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?
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Solution
Median is the middle value, which is 8.
Correct Answer:
A
— 8
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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?
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Solution
The sum of deviations from the mean is always 0.
Correct Answer:
A
— 0
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Showing 1 to 30 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.
