Given a distribution mean of 14 and standard deviation of 5, calculate its coefficient of variation?
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Answer: C. 35.7%
Explanation
The coefficient of variation is calculated by dividing standard deviation by mean and multiplying by one hundred. Dividing five by fourteen yields approximately zero point three five seven one for the ratio. Multiplying this decimal value by one hundred produces the final percentage of thirty-five point seven. The coefficient of variation provides a dimensionless measure of dispersion for comparing different datasets. It is particularly useful when comparing the variability of variables measured in different measurement units. Higher percentage values indicate greater relative data dispersion around the arithmetic mean.
Financial analysts use this metric to compare investment risk relative to expected asset returns. Biologists apply the coefficient of variation to compare morphological trait variability across animal species. Using relative dispersion prevents misleading conclusions caused by differences in data scale or units. Option A overestimates the relative variation because the calculation formula was applied incorrectly. Option B represents an incorrect arithmetic ratio resulting from erroneous division or multiplication steps. Option D is mathematically incorrect and does not match the correct division and scaling result.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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