The only Frederick I can find living Liverpool in 1871 is aged 25 (born c 1846) and is a boarder, Married and is a train driver. No family living with him.
Other possibilities are aged 33 living Southport (joiner)with family but no Mary Ann
All the Mary Ann (Mary, Mary A or Mary Anne) born liverpool between 2-5 are living in households with parents resident and none are Frederick, sorry.
The only other possibility is the following
Elizabeth Ellis 32 Liverpool Head
Mary J Ellis 2 Liverpool Daughter
No male relative in household
Robraw