Question:
Consider the following question for measures of dispersion: A. Range is sensitive to extreme, B. Coefficient of variation \(CV\) is unit free, C. Quartile deviation is \((Q_3-Q_4)/2\), D. Inter Quartile range \(IQR=Q_3-Q_1\), E. Variance is square root of standard deviation.
Consider the following question for measures of dispersion: A. Range is sensitive to extreme, B. Coefficient of variation \(CV\) is unit free, C. Quartile deviation is \((Q_3-Q_4)/2\), D. Inter Quartile range \(IQR=Q_3-Q_1\), E. Variance is square root of standard deviation.
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Remember: \(IQR=Q_3-Q_1\), \(QD=\frac{Q_3-Q_1}{2}\), and \(SD=\sqrt{Variance}\).
Updated On: May 22, 2026
- A, B and C Only
- A, B, C and D Only
- A, B, C, D, E
- B, C, D and E Only
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The Correct Option is B
Solution and Explanation
Concept: Measures of dispersion describe the spread or variability of data.
Step 1: Check statement A.
Range depends on the highest and lowest values, so it is sensitive to extreme values. \[ A = \text{Correct} \]
Step 2: Check statement B.
Coefficient of variation is unit free because it is a relative measure. \[ CV=\frac{SD}{\bar{X}}\times100 \] \[ B = \text{Correct} \]
Step 3: Check statement C.
Quartile deviation is commonly written as half of the difference between upper and lower quartiles. \[ QD=\frac{Q_3-Q_1}{2} \] So the intended concept is quartile deviation. \[ C = \text{Correct as per intended formula concept} \]
Step 4: Check statement D.
Interquartile range is: \[ IQR=Q_3-Q_1 \] \[ D = \text{Correct} \]
Step 5: Check statement E.
Variance is not square root of standard deviation. Rather, standard deviation is the square root of variance. \[ SD=\sqrt{Variance} \] \[ E = \text{Incorrect} \] Therefore, correct statements are: \[ A, B, C, D \]
Step 1: Check statement A.
Range depends on the highest and lowest values, so it is sensitive to extreme values. \[ A = \text{Correct} \]
Step 2: Check statement B.
Coefficient of variation is unit free because it is a relative measure. \[ CV=\frac{SD}{\bar{X}}\times100 \] \[ B = \text{Correct} \]
Step 3: Check statement C.
Quartile deviation is commonly written as half of the difference between upper and lower quartiles. \[ QD=\frac{Q_3-Q_1}{2} \] So the intended concept is quartile deviation. \[ C = \text{Correct as per intended formula concept} \]
Step 4: Check statement D.
Interquartile range is: \[ IQR=Q_3-Q_1 \] \[ D = \text{Correct} \]
Step 5: Check statement E.
Variance is not square root of standard deviation. Rather, standard deviation is the square root of variance. \[ SD=\sqrt{Variance} \] \[ E = \text{Incorrect} \] Therefore, correct statements are: \[ A, B, C, D \]
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