Calculus from a Statistics Perspective
  This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function defined by data or sampling values from a given function, rather than an explicit mathematical formula. The basics of this approach are two averages: arithmetic mean and graphic mean. The arithmetic mean is used to define integral. Area is used to interpret the meaning of an integral. Antiderivative is introduced from integral, and derivative-antiderivative pair is introduced as a mathematical operation entity. The graphic mean is an average speed in an interval and is used to interpret the meaning of a derivative. 
Samuel S.P. Shen, Dov Zazkis, Kimberly Leung, and Chris Rasmussen
math.HO