UNITED NATIONS — Dire poverty has dropped sharply, and just as many girls as boys are now enrolled in primary schools around the world. Simple measures like installing bed nets have prevented some six million deaths from malaria. But nearly one billion people still defecate in the open, endangering the health of many others.

These are among the findings that the United Nations released Monday as part of a final report on the successes and failures of the Millennium Development Goals, a set of targets established 15 years ago to improve the lives of the poor.

“The report confirms that the global efforts to achieve the goals have saved millions of lives and improved conditions for millions more around the world,” the United Nations secretary general, Ban Ki-moon, said Monday as he released the report in Oslo.

In fact, though, how much of those gains can be attributed to the goals is unknown. The sharp reductions in extreme poverty are due largely to the economic strides made by one big country, China. Likewise, some of the biggest shortfalls can be attributed to a handful of countries that remain very far behind. In India, for example, an estimated 600 million people defecate in the open, heightening the risk of serious disease, especially for children.