The cost of getting an M.B.A. has risen sharply in recent years. Now the Education Department is providing an in-depth look at how much government debt students who pursue the degree are taking on.

Data released by the department show that roughly 92,800 people who took out federal student loans and graduated with a master’s degree in business administration in 2016 and 2017 together had about $3.7 billion in such loans.

The...