Don't know if you already know this but here goes. According to the 1880 census Ann was only 15 years old so she married Arthur 10 years her senior. Ann and her parents were born in Wales. BY the 1900 census she has died as Arthur has a second wife named Henrietta and 3 kids by her. Three sons from his first wife are living with them. I looked at all Rodgers born in Wales in Illinois in 1870 and none had a daughter age 5 born Wales? They may not have immigrated to this country until after 1870 so placing Ann in one of the Rodgers families in the 1880 census from Wales will be impossible as she is already married and out of their household.