For years, China’s statistics bureau has faced doubts among analysts about the reliability of its data. Now, the ruling Communist Party itself is raising an eyebrow, questioning the quality of the bureau’s statistics as well as some of the profits made off these official numbers.

More than 300 cadres at the National Bureau of Statistics made personal gain by charging fees for providing data, research and other services, the party’s antigraft inspectors found during a probe into the bureau between November and December last...