Statistics are supposed to make the interpretation of data easier to understand. However, statistics can be used to mislead casual observers into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In (many) others, it is purposeful and for the gain of the perpetrator (and often based on their biases and their own beliefs). When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.
More generally, statistical fallacies can be seen as an entire class of fallacies that result in presenting statistical data in a very biased way and interpreting statistics without questioning the methods behind the collection and presentation of the data.
Here’s an example in its logical form:
1) Claim A is made.
2) Statistic S is manipulated to support claim A.
An example? See below.