This appears to be the family in the 1880 USA Census, available on the LDS Family Search site-
Name: William M. Dunsmore Event Type: Census Event Date: 1880 Event Place: Covington, Tioga, Pennsylvania, United States Gender: Male Age: 23 Marital Status: Single Occupation: Farm Laborer Race (Original): Ethnicity: American Relationship to Head of Household: Son Birthplace: Pennsylvania, United States Birth Date: 1857 Spouse's Name: Spouse's Birthplace: Father's Name: John Dunsmore Father's Birthplace: Scotland Mother's Name: Janet Dunsmore Mother's Birthplace: Scotland Page: 118 Page Letter: C Entry Number: 304 Affiliate Film Number: T9-1197 GS Film number: 1255197 Digital Folder Number: 004244562 Image Number: 00782 Household Gender Age Birthplace Self John Dunsmore M 46 Scotland Wife Janet Dunsmore F 41 Scotland Son William M. Dunsmore M 23 Pennsylvania, United States Daughter Kate Dunsmore F 21 Pennsylvania, United States Son Andrew Dunsmore M 15 Pennsylvania, United States Daughter Jane Dunsmore F 13 Pennsylvania, United States Son John C. Dunsmore M 11 Pennsylvania, United States Son James Dunsmore M 9 Pennsylvania, United States Son Albert Dunsmore M 7 Pennsylvania, United States Daughter Nellie Dunsmore F 4 Pennsylvania, United States Son Charles Dunsmore M 0 Pennsylvania, United States
In the 1851 UK Census, there are the following JD entries of the right age
www.scotlandspeople.gov.uk or www.findmypast.co.uk
Household DUNSMORE, John 1833 18 M Greenock RenfrewshireVIEWN/A Household DUNSMORE, John 1835 16 M Middle Ward LanarkshireVIEWN/A Household DUNSMORE, John 1833 18 M Rutherglen LanarkshireVIEWN/A Household DUNSMORE, John 1833 18 M Kyle AyrshireVIEWN/A Household DUNSMORE, John 1834 17 M Tintock Twechar & C DunbartonshireVIEWN/A Household DUNSMORE, John 1835 16 M Tibbermore PerthshireVIEWN/A Household DUNSMORE, John 1836 15 M Kilmarnock AyrshireVIEWN/A Household DUNSMORE, John 1835 16 M Peebles PeeblesshireVIEWN/A
The last one lives and works on a farm BUT That is NO GUARANTEE that he is the one you seek.
Tou should follow through first in the later American Records, as some have more precise in formation about the Births of Individuals - particul;arly Death Records.