There is an Ann WATSON age 15 in the 1851 census on familysearch , described as niece, house servant living in Usworth, Chester-le-Street DUR, born Durham HO107/2394/595/8. Unfortunately I can't tell who she is staying with.
The one in Usworth in 1851 was niece to John & Jane Armstrong. From the birth of their youngest child, George E Armstrong aged 5, Jane's maiden surname appears to be Graham.
In 1841 I think this particular Ann is in Framwellgate, Durham with William & Ann Watson:
William Watson 40
Ann Watson 40
James 20
Foster 15
William 15
John 13
Jane 12
George 10
Ann 5
Richard 6 Mo
WATSON, RICHARD MMN: GRAHAM
GRO Reference: 1841 M Quarter in CHESTER LE STREET Volume 24 Page 29
In 1851 William, Ann & George are also in Usworth, Richard having died in 1845.
William Watson 57 Head b Lamesley, Durham Coal Miner
Ann Watson 50 b Gateshead, Durham
George Watson 19 b Pensher [Penshaw], Durham Coal Miner