The value of coefficient of variation exceeds 100%, when:

Question

Accepted Answer

The correct option is 2:

The Coefficient of Variation (CV) is a standardized measure of dispersion of a probability distribution or frequency distribution. It is widely used in statistics to compare the variability or risk of two or more data sets, even if their means are drastically different. The formula for the Coefficient of Variation is:

$$CV = (\frac{\sigma}{\bar{X}}) 	imes 100$$

Where $\sigma$ (sigma) represents the standard deviation (the absolute measure of variability), and $\bar{X}$ (X-bar) represents the arithmetic mean (average) of the data. For the value of the CV to exceed 100%, the ratio $(\frac{\sigma}{\bar{X}})$ must be greater than 1. This condition is mathematically satisfied only when the standard deviation ($\sigma$) is greater than the mean ($\bar{X}$). When the variability (standard deviation) is larger than the average value of the data set, it signifies extremely high relative dispersion, pushing the coefficient of variation above 100%.

The incorrect option is 1:
The option $\sigma \< \bar{X}$ implies that the standard deviation is less than the mean. In this case, the ratio $(\frac{\sigma}{\bar{X}})$ will be less than 1, and consequently, the Coefficient of Variation will be less than 100%. This represents a relatively low level of dispersion in the data set.

The incorrect option is 3:
The option $\sigma = \bar{X}$ means the standard deviation is exactly equal to the mean. Substituting this into the CV formula, the ratio $(\frac{\sigma}{\bar{X}})$ becomes 1, which results in a Coefficient of Variation of exactly 100%.

The incorrect option is 4:
The option $\sigma \leq \bar{X}$ covers two scenarios: $\sigma \< \bar{X}$ (CV \< 100%) and $\sigma = \bar{X}$ (CV = 100%). In neither of these cases does the Coefficient of Variation exceed 100%.