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 0.819 0.164 0.937 Malic Acid 0.329 0.869 0.368 Ash 0.248 0.186 0.393 Alkalinity 0.677 0.523 0.249 Magnesium 0.643 0.075 0.573 Phenols 0.825 0.977 0.034 Flavonoids 0.896 1.212 0.083 Nonflavonoids 0.595 0.724 0.009 Proanthocyanidins 0.619 0.778 0.010 Color Intensity 0.135 0.939 0.881 Hue 0.497 1.162 0.437 Dilution 0.744 1.289 0.295

Proline 1.117 0.406 0.776

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 1.089 Malic Acid 0.546 Ash 0.017 Alkalinity 0.534 Magnesium 1.308 Phenols 1.028 Flavonoids 0.065 Nonflavonoids 0.614 Proanthocyanidins 0.295 Color Intensity 0.863 Hue 0.645 Dilution 0.491 Proline 0.056

Calculate the following Euclidean distances. (Round your answers to three decimal places.) Euclidean distance from new wine and Cluster 1: _________ Euclidean distance from new wine and Cluster 2: _________

Euclidean distance from new wine and Cluster 3: :_________

In which cluster of wines should he place this new wine?