Measures of Dispersion for Competitive Exam Success

Measures of Dispersion

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%

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%

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?

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

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

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?

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

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

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

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

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

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%

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

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

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%

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?

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. 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%

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%

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:

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

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%

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:

A. 8
B. 6
C. 4
D. 2

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?

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

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}?

A. 40
B. 30
C. 50
D. 20

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 5?

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

Solution

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.

Correct Answer: B — 10%

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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%

Solution

Coefficient of variation = (Standard deviation / Mean) * 100 = (10 / 50) * 100 = 20%.

Correct Answer: A — 20%

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Q. What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?

A. 4
B. 6
C. 8
D. 10

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}?

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

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}?

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

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?

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

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?

A. 4
B. 6
C. 8
D. 10

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}?

A. 5
B. 3
C. 4
D. 7

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?

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

Solution

The mode is the number that appears most frequently, which is 4.

Correct Answer: D — 4

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Measures of Dispersion

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