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Why is the coefficient of variation used when comparing two data sets?
AIt adjusts for a difference in the scale of the data
BIt removes the effect of any outlier in the data
CIt converts the median into a percentage figure
DIt replaces the standard deviation with the range
Answer & Solution
Correct answer: A. It adjusts for a difference in the scale of the data
1. A given amount of variation means something different around a large mean than around a small one.
2. The coefficient of variation divides the standard deviation by the mean and multiplies by 100.
3. Both sets are then expressed on the common scale of a percentage of their own mean, so their variability can be compared directly.
4. It does nothing about outliers, which continue to inflate the standard deviation in the numerator.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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