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LOS ANGELES — California officials estimate that the U.S. Census Bureau failed to count 1.5 million of the state’s residents, a discrepancy that if true could cost the state billions of dollars in federal aid over the next decade and perhaps an increase in its representation in Congress.

On Tuesday, the Census Bureau released population figures that showed California to have 37.3 million residents, 10 percent more than in 2000. But according to the state Department of Finance, the state’s population was 38.8 million on July 1. That figure is drawn from birth and death statistics, school data, driver’s license address changes, tax returns and Medicare enrollment, a “more refined” picture of the population, according to H.D. Palmer, a department spokesman.

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