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.

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
MalicAcid ...................................... 20.480
Ash .................................................. 0.049
Alcalinity ......................................... 0.600
Magnesium .................................. 21.242
Phenols ........................................... 1.094
Flavanoids ....................................... 0.001
Nonflavanoids ................................ 0.548
Proanthocyanins ......................... 20.229
ColorIntensity ............................... 20.797
Hue .................................................. 0.711
Dilution .......................................... 20.425
Proline ............................................. 0.010

Characteristic Cluster 1 Cluster 2 Cluster 3 0.819 Alcohol 0.164 -0.937 -0.368 MalicAcid -0.329 0.869 0.248 0.186 Ash -0.393 Alcalinity Magnesium -0.677 0.523 0.249 0.643 -0.075 -0.573 Phenols 0.825 0.977 -0.034 Flavanoids -1.212 0.083 0.896 Nonflavanoids -0.595 0.724 0.009 0.619 Proanthocyanins Colorintensity -0.778 0.010 0.135 0.939 -0.881 0.437 Hue 0.497 - 1.162 Dilution 0.744 -1.289 0.295 -0.776 Proline 1.117 -0.406