I was wondering how the variable SCH_DEG from College Scorecard was derived. What does it mean to be the degree prominently awarded in terms of the actual #'s? Is it > 50% or more than that?

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It's the type of degree that makes up a larger percentage than any other.

From the documentation:

Predominant undergraduate degree (PREDDEG) identifies the type of degree that the institution primarily awards; for instance, an institution that awards 40 percent bachelor’s degrees, 30 percent associate degrees, and 30 percent certificate programs would be classified as predominantly bachelor’s degree awarding

SCH_DEG is PREDEG with missing values imputed.

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