I think you'll find that Ann was much older than she admitted to. You don't say that the 1861 and 1871 census state she was born in Meriden, Warwickshire.
In 1871 she is 37 (bc.1834), in 1861 she is 30 (bc.1831) and I believe she was a servant in Edgbaston in 1851 aged 25!
There was only one Humphrey Harper in Meriden having children baptised at the relevant period and this baptism for Ann - and age given in 1851 - would tie in with this:
Ann Harper bp.22/5/1825 Meriden, Warwickshire, dau. of Humphrey and Elizabeth - siblings all baptised at Meriden:
Susanna bp.13/9/1814
Elizabeth bp.18/2/1816
Thomas bp.23/5/1819
Mary bp.9/11/1823
Jane bp.29/7/1828
Richard bp.7/8/1831
Maria bp.8/3/1835
Humphrey Harper married Elizabeth Horton 22/11/1813 Birmingham, Warwickshire
Census shows Humphrey was bc.1784 Meriden and his wife Elizabeth bc.1793 Birmingham.
Humphrey Harper bp.12/1/1785 Meriden, son of Humphrey and Jane.
Annette