This problem does not require the use of data mining software and focuses on knowledge of concepts and basic calculations.

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: