Von Brandenstein (1980:2) identifies Norseman as one of six language varieties in the Dundas District area (the others being Mirning (Eucla) A9, Marlba A110, Fraser Range A74, Windaga A111 and Kallaagu A2. He does comment, though, that 'it will be difficult to extract the different components of the Dundas District languages ... from the mixed language now called Ngadju A3 which is still spoken...' and notes that Norseman is covered by the area identified as Gala:gu A2 by O'Grady in Capell (1963).
Von Brandenstein may have collected data (1966, 1970, 1970). However, with so little information (no name is given, only a locational descriptor) and no language data, Norseman is described as Unconfirmed.
From Norseman to Fraser Range (von Brandenstein 1980:2).
Speaker numbers were measured differently across the censuses and various other sources listed in AUSTLANG. You are encouraged to refer to the sources.
Speaker numbers for ‘NILS 2004’ and ‘2005 estimate’ come from 'Table F.3: Numbers of speakers of Australian Indigenous languages (various surveys)' in 'Appendix F NILS endangerment and absolute number results' in McConvell, Marmion and McNicol 2005, pages 198-230 (PDF, 2.5MB).