NEW YORK — Although the United States no longer leads the world in educational attainment, record numbers of young Americans are completing high school, going to college, and finishing college, according to a Pew Research Center analysis of newly available census data.

This year, for the first time, a third of the nation’s 25- to 29-year-olds have earned at least a bachelor’s degree. That share has been slowly edging up for decades, from less than one-fifth of young adults in the early 1970s to 32 percent last year.