Descriptive Statistics - Why do we need to study the variation of a collection

Descriptive Statistics

1. Why do we need to study the variation of a collection of data? Why isn’t the average by itself is adequate? This week in chapter 4 (course textbook), we have studied three ways to measure variations.  The range, standard deviation, and to a large extent, a box-and-whisker plot all indicate the variation within a data collection.  Discuss the similarities and differences among these 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?