I have the common misconception in my business calculus classes that the Average Rate of Change, say from $x=1$ to $x=5$, is the statistical average of the rates on the four unit intervals $1$ to $2$, $2$ to $3$, etc. So when introducing/reviewing Average Rate of Change, I'm tempted to say "This is not an Average like you learn about in your stats class." Except, in reality, it is. From the perspective at the end of the course, the difference quotient is the result of finding the average value of the derivative. And the idea of the average value of a continuous function is very much like the averages they compute in a stats class.
So my question is: How can I tell them not to compute a statistical average without lying to them about the relation between average rate of change and continuous statistics?