WASHINGTON — The Obama administration on Friday unveiled data showing that many Americans with health insurance bought under the Affordable Care Act could face substantial price increases next year — in some cases as much as 20 percent — unless they switch plans.

The data became available just hours before the health insurance marketplace was to open to buyers seeking insurance for 2015.

An analysis of the data by The New York Times suggests that although consumers will often be able to find new health plans with prices comparable to those they now pay, the situation varies greatly from state to state and even among counties in the same state.