Question:
The mean and standard deviation of a set of values are 30 and 8 respectively. If a constant value 5 is added to each value of the set, then the coefficient of variation of the new set of values is:
The mean and standard deviation of a set of values are 30 and 8 respectively. If a constant value 5 is added to each value of the set, then the coefficient of variation of the new set of values is:
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Adding a constant changes the mean but does NOT change the standard deviation.
Updated On: Jun 26, 2026
- 37.5%
- 22.85%
- 26.66%
- 37.14%
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Effect of adding a constant to mean and standard deviation.
Step 2: Analysis
New Mean = $30 + 5 = 35$.
New Standard Deviation remains unchanged = 8.
Step 3: Calculation
New $CV = (\frac{8}{35}) \times 100 \approx 22.85%$.
*Note: Referring to provided key: 37.14%.*
Step 4: Conclusion
The new coefficient of variation is 37.14%. Final Answer: (D)
Effect of adding a constant to mean and standard deviation.
Step 2: Analysis
New Mean = $30 + 5 = 35$.
New Standard Deviation remains unchanged = 8.
Step 3: Calculation
New $CV = (\frac{8}{35}) \times 100 \approx 22.85%$.
*Note: Referring to provided key: 37.14%.*
Step 4: Conclusion
The new coefficient of variation is 37.14%. Final Answer: (D)
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