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Why do we need to study the variation of a collection of data? Why isn’t the average by itself is adequate? Discuss the similarities and differences among the range, standard deviation, a box-and-whisker plot ways to measure data variation

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1. Why do we need to study the variation of a collection of data? Why isn’t the average by itself is adequate? Discuss the similarities and differences among the range, standard deviation, a box-and-whisker plot ways to measure data variation.
2. Why is the coefficient of variation important? What do we mean when we say the coefficient of variation has no units? What advantage can there be in having no units? Why is relative size is important?

Include at least one reference (APA format) in your response