I didn't find the answer either but hopefully I found more Census info which might provide you more clues.
First I found the Furman Family on the Taylor Family Tree on Ancestry. I asked the owner to contact you but if they don't, you can access the tree by signing up for a free 14-day trial. Just be sure to cancel on day 13.
In 1880 the Furman family was living in Lyon, Hamilton Co., IA.
Anesley A. Furman, head household, b. PA, 28, farmer.
Mary P., mother, b. NY state, 56, div.
James L., brother, b. PA, 21, farmer.
Elmer, brother, b. PA, 17, herding cattle.
Willie A., brother, b. IA, 15, farm laborer.
Hammond Ricks, hired man.
In 1900 William, Katie, Martha and Earl lived in Rushville, Sheridan Co., NE.
In 1910 William was living in Montrose, Montrose Co., CO.
William A. Furman, b. IA, 45, M1 23 yrs, both parents born in PA, farm/orchard laborer.
In 1920 William A. Furman was living in Ouray, Ouray Co., CO.
William A. Furman, b. IA, 59, divorced, both parents b. PA, blacksmith own shop.
In 1930 William and his wife Lucinda and EArl and his wife Rose were living in Ouray.
William Furman, b. IA, 68, both parents b. PA, blacksmith own shop.
Lucinda, wife, b. MO, 75.
EArl Furman, b. NE, 30, marr @ 22, blacksmith shops.
Rose, wife, b. KS, 26, marr @ 18. Successful Searching!
In 1885 the Furman family was living in Liberty, Hamilton Co., Iowa.
Mary P. Furman, b. PA, 57, div.
James L., b. PA, 26, married.
Hellen L., b. WI, 25, James's wife.
Elmer, son, b. WI, 21, farmer.
William A., son, b. IA, 19.