Distance to Centroid Calculation for Wine Clusters. Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table. Characteristic Cluster $1$ Cluster $2$ Cluster $3$ Alcohol $0\mathrm{.}8190\mathrm{.}16420\mathrm{.}937$ Malic Acid $20\mathrm{.}3290\mathrm{.}86920\mathrm{.}368$ Ash $0\mathrm{.}2480\mathrm{.}18620\mathrm{.}393$ Alkalinity $20\mathrm{.}6770\mathrm{.}5230\mathrm{.}249$ Magnesium $0\mathrm{.}64320\mathrm{.}07520\mathrm{.}573$ Phenols $0\mathrm{.}8250\mathrm{.}97720\mathrm{.}034$ Flavanoids $0\mathrm{.}89621\mathrm{.}2120\mathrm{.}083$ Nonflavanoids $20\mathrm{.}5950\mathrm{.}7240\mathrm{.}009$ Proanthocyanins $0\mathrm{.}61920\mathrm{.}7780\mathrm{.}010$ Color Intensity $0\mathrm{.}1350\mathrm{.}93920\mathrm{.}881$ Hue $0\mathrm{.}49721\mathrm{.}1620\mathrm{.}437$ Dilution $0\mathrm{.}74421\mathrm{.}2890\mathrm{.}295$ Proline $1\mathrm{.}11720\mathrm{.}40620\mathrm{.}776$ Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations. Characteristic Alcohol $21\mathrm{.}023$ Malic Acid $20\mathrm{.}480$ Ash $0\mathrm{.}049$ Alkalinity $0\mathrm{.}600$ Magnesium $21\mathrm{.}242$ Phenols $1\mathrm{.}094$ Flavanoids $0\mathrm{.}001$ Nonflavanoids $0\mathrm{.}548$ Proanthocyanins $20\mathrm{.}229$ Color Intensity $20\mathrm{.}797$ Hue $0\mathrm{.}711$ Dilution $20\mathrm{.}425$ Proline $0\mathrm{.}010$ using excel