Two key questions in Clustering problems are how to determine the number of groups properly and measure the strength of group-assignments. These questions are specially involved when the presence of certain fraction of outlying data is also expected. Any answer to these two key questions should depend on the assumed probabilisticmodel, the allowed group scatters and what we understand by noise. With this in mind, ∗Research partially supported by the Spanish Ministerio de Ciencia e Innovación, grant MTM2008-06067C02-01, and 02 and by Consejeŕıa de Educación y Cultura de la Junta de Castilla y León, GR150. †Departamento de Estad́ıstica e Investigación Operativa. Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain.