In some cases, statistics may be persuasive since, in most cases, statistics involve numbers and

In some cases, statistics may be persuasive since, in most 
cases, statistics involve numbers and or facts, and thus most people use them to provide convincing information about 
certain things.
There is a certain “gravitas” associated with numbers. If we see numbers, we tend to believe the arguments much more easily. 
Unfortunately, this leads to people abusing numbers. This is 
either done by intended unethical manipulation of the data or 
by accidentally incorrectly gathering or analyzing the data.
This is why reputation is so important in the sciences. One 
needs to trust the source.