Hello Norma,
Could this be your grandmother in the 1881 census:-
Dwelling: 17 Lodge Street
Census Place: Failsworth, Lancashire, England
Source: FHL Film 1341962 PRO Ref RG11 Piece 4028 Folio 146 Page 28
Marr Age Sex Birthplace
Thomas BEBBINGTON M 40 M Eccleston, Lancashire, England
Rel: Head
Occ: Carpenter & Wheelwright
Rebecca BEBBINGTON M 40 F Northwold, Norfolk, England
Rel: Wife
John Wm. BEBBINGTON 13 M Manchester, Lancashire, England
Rel: Son
Occ: Scholar
Caroline TUDDENHAM 5 F Longtown, Cumberland, England
Rel: Niece
Harry