k-Means Clustering of Wines. Amanda Boleyn, an entrepreneur who recently sold her start-up for a multi-million-dollar sum, is looking for alternate investments for her newfound fortune. She is considering

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k-Means Clustering of Wines. Amanda Boleyn, an entrepreneur who recently sold

her start-up for a multi-million-dollar

sum, is looking for alternate investments for her

newfound fortune. She is considering an investment in wine, similar to how some people

invest in rare coins and fine art. To educate herself on the properties of fine wine, she has

collected data on 13 different characteristics of 178 wines. Amanda has applied k-means

clustering to this data for k 5 1, . . . , 10 and generated the following plot of total sums

of squared deviations. After analyzing this plot, Amanda generates summaries for k 5 2,

3, and 4. Which value of k is the most appropriate to categorize these wines? Justify your

choice with calculations.

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