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 |
| Flavanoids | 0.896 | -1.212 | 0.083 |
| Nonflavanoids | -0.595 | 0.724 | 0.009 |
| Proanthocyanins | 0.619 | -0.778 | 0.01 |
| 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. (hint: distance between two clusters based on the centroids can be calculated using )
| Characteristic | New Wine |
| Alcohol | -1.023 |
| Malic Acid | -0.480 |
| Ash | 0.049 |
| Alkalinity | 0.600 |
| Magnesium | -1.242 |
| Phenols | 1.094 |
| Flavanoids | 0.001 |
| Nonflavanoids | 0.548 |
| Proanthocyanins | -0.229 |
| Color Intensity | -0.797 |
| Hue | 0.711 |
| Dilution | -0.425 |
| Proline | 0.010 |
