A number repeated confidently gains familiarity before it gains accuracy.

Repetition does something to a figure that has nothing to do with whether it is right. Hearing it three times makes it feel settled, and once it feels settled people stop asking where it came from and start building arguments on top of it. Confidence in the delivery speeds this up. By the time anyone checks, the number has acquired a life that does not depend on the check.

When a striking figure turns up, spend one minute looking for its source before passing it on. And if you find yourself quoting something you cannot trace, say so, which costs little and keeps the room honest.