Hi Janet,
Are you sure the surname is Norris? On the 1881 and particularly the 1891 censuses it appears to be Morris. Freebmd doesn't have a birth reference for an Andrew Norris in Glamorgan, but does have an Andrew Morris born 1866 with a Merthyr registration.
The enumerator's handwriting in 1871 is virtually illegible. The family are in Merthyr, but I can't make out the address. Family mambers not included in 1881 are father, James aged 44, born Radnorshire and sons, Richard aged 17, John aged 10 and another son ? David aged ?12.
Ref: RG10/5399, folio 155, pg. 29, sch. 148
In 1891 the family are at 10 Pant Rd., Merthyr. In addition to mother Elizabeth, are sons James & Andrew, daughter, Sarah and a nephew called Richard aged 11 along with a niece called Martha aged ?
Ref: RG12/4439, folio 135, pg.21
Cwmaman