Question: 2. Distance to Centroid Calculation for Wine Clusters. Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average

2. 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 0.819 0.164 20.937 Malic Acid 20.329 0.869 20.368 Ash 0.248 0.186 20.393 Alkalinity 20.677 0.523 0.249 Magnesium 0.643 20.075 20.573 Phenols 0.825 0.977 20.034 Flavanoids 0.896 21.212 0.083 Nonflavanoids 20.595 0.724 0.009 Proanthocyanins 0.619 20.778 0.010 Color Intensity 0.135 0.939 20.881 Hue 0.497 21.162 0.437 Dilution 0.744 21.289 0.295 Proline 1.117 20.406 20.776 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 21.023 Malic Acid 20.480 Ash 0.049 Alkalinity 0.600 Magnesium 21.242 Phenols 1.094 Flavanoids 0.001 Nonflavanoids 0.548 Proanthocyanins 20.229 Color Intensity 20.797 Hue 0.711 Dilution 20.425 Proline 0.010

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