About a third of recent for-profit college graduates attended career-training programs whose typical graduate annually earns less than the federal minimum wage, new federal data show. Vocational programs, common at community colleges and for-profit schools, are meant to help graduates land well-paying jobs. But of Americans who graduated from such programs at for-profits from 2008 to 2012, some 32 percent attended programs in which a typical graduate made less than $14,500—what a full-time worker making the federal minimum wage would earn—in 2014, even as they incurred student debt, federal officials said. Just 14 percent of those from public schools’ vocational programs, by contrast, graduated from programs whose typical graduates made so little. That data led officials to declare Thursday that public schools provide far better value for students and the taxpayers who subsidize their studies. … In a prepared statement, Steve Gunderson, who leads Career Education Colleges & Universities, the for-profit college trade group, called it “absolutely absurd to compare totally different fields of study and suggest that programs traditionally taught in public institutions have higher incomes than programs taught in proprietary colleges.” But the new federal data threaten to intensify pressure on for-profit colleges, whose enrollment and share prices dropped sharply during the Obama administration amid government investigations and lawsuits alleging fraud. Recent research has found that Americans who attended for-profit colleges were, on average, worse off for having enrolled—a finding the industry rejects.