The coefficient of variation is useful when:
I. The frequency distribution contains open-ended classes or overlapping classes.
II. The data sets being compared contain data in different measurement units.
III. The data sets being compared contain data with similar measurement units.
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A. B. C. D. E.D
The coefficient of variation is useful when the means of the data sets are widely different or when the observations are in different measurement units.
The coefficient of variation (CV) is a statistical measure that is used to compare the relative variability or dispersion of data sets. It is defined as the ratio of the standard deviation to the mean, expressed as a percentage. The CV provides a standardized measure of dispersion that allows for the comparison of data sets with different means and standard deviations.
Let's evaluate each statement and determine when the coefficient of variation is useful:
I. The frequency distribution contains open-ended classes or overlapping classes. The coefficient of variation can be useful when dealing with frequency distributions that contain open-ended classes or overlapping classes. In such cases, the standard deviation alone may not provide an accurate comparison of variability between data sets. The CV takes into account the relative dispersion in relation to the mean, making it a better measure of relative variability in these situations. Therefore, statement I is true.
II. The data sets being compared contain data in different measurement units. The coefficient of variation is particularly useful when comparing data sets that are measured in different units. Since the CV is a relative measure, it standardizes the dispersion regardless of the measurement units. By using the CV, we can compare the relative variability of data sets with different means and standard deviations, making statement II true.
III. The data sets being compared contain data with similar measurement units. When the data sets being compared have similar measurement units, the coefficient of variation is less useful. In such cases, the standard deviation alone may be sufficient to compare the variability between the data sets. The CV becomes more valuable when comparing data sets with different measurement units or different scales. Therefore, statement III is false.
Based on the analysis above, the correct answer is: B. I & II
The coefficient of variation is useful when the frequency distribution contains open-ended classes or overlapping classes (statement I) and when the data sets being compared contain data in different measurement units (statement II).