I think that this Douglas was s/o John & Christina (Tullis) Osborn. I believe a few pages away in the census is Douglas's brother Caleb age 51.

I'm just now searching for information on this, so what I have at this point is a bit sketchy, but here is what I have found so far.

Clinton Co marriage records lists:
Cristina A. Tullis married a John H. Osborn Nov 11 1852.
Christenia A. Osborn married a John Osborn Sep 12 1867
(unsure yet if this is same Christina and then is it a different John Osborn?)
Christenia A. Osborn married Jackson Boorom Dec 2 1878 in Clinton Co.

With the help of Liz Osborn I was able to locate John & Christina Osborn in 1870:
1870 Ohio, Clinton, Marion, Blanchester Town
Page 574 (Ancestry.com image 6)
Lines 17-21, Dwelling 249, Household 256
Osborn, John; 55, M W Retired Farmer, $5000/1000, Ohio
Christena; 38, F W Keepse (sic) House; Ohio
Duglas, 9 M W Ohio *
John, 5 M W Ohio
Caleb, 1 M W Ohio

1880 Census OH Clinton Co., Marion Twp. pg 117C lists:
Boorom, Jackson age 65 b. OH both parents born OH Occ: farmer
Boorom, Christine wife age 48 b. OH both parents b. OH
Osborn, Theodore (sic) step son age 1 (sic) b. OH both parents b. OH
Osborn, John step son age 14 b. OH both parents b. OH
Osborn, Calop E step son age 11 b. OH

A few pages away 116 B living with a Hudson family is:
Osborn, Douglas age 17 b. OH both parents b. OH Occ: farm Laborer

My interest began with Jackson Boorom, wondering if he is same Jackson s/o Aaron
Booram & Elizabeth Heck in Symmes Twp. Hamilton Co., OH, married Sarah Jane Cook 1843 in Warren Co., living 1850 in Hamilton Co., 1860 & 1870 in Turtle Creek Twp.,
Warren Co.

Checking the 1850 census I found a Christina Tullis with parents Peter & Elizabeth (Cook) Tullis age 18. Now, it just so happens that Jackson’s 1st wife Sarah Cook was half
sister of Elizabeth Cook Tullis (father was Conrad Cook), so it would appear that the Jackson Boorom who married Christina Osborn is who I thought he was!

Still haven’t figured out the John Osborn’s, nor have I found a John with a Christina in 1860 (looking in Warren & Clinton Co’s) but am currently looking for this information.
Would love to compare notes/info.
Linda Boorom