The number of Americans without health insurance fell by 3.8 million in early 2014, according to new federal figures. The first government analysis of how the Affordable Care Act has affected insurance-coverage rates showed that the percentage of people without health insurance dropped from an average of 14.4 percent to 13.1 percent in the first three months of this year. About 3.7 million people in the survey said they obtained private coverage through online exchanges run by states and the federal government. The tally of people who acquired coverage could be low because the survey might not reflect a late surge in enrollment. The study mirrors some outside findings: Gallup has reported that the number had fallen to 13.4 percent in the second quarter of 2014. The Obama administration announced that more than 8 million people bought coverage through the exchanges.