Question- Race

Hola Members, I have been playing with my wifes side of the family (with no luck) I found My wifes Grandmother -TRANQUILINA VASQUEZ- in the 1910 census located in El Paso ,Texas . They have Tranquilina at approxitemately 10 years of age . Any way I was tripping because they have her classified as a octoroon(1/8 th black). No big deal just trying to figure out how did the census figure this racial composition . In 1910 they didn't have any DNA testing and didn't know her family backround . I was just trying to figure this out how they did it. I also wanted to know how I access or where to go for immigration or border crossing info so I can obtain where Tranquilina Vasquez was born . (parents -I believe were Pedro Vasquez and Matilde Ceniceros -from Chihuahua)
Thanks
Ronnie