Calculus from a Statistics Perspective

TL;DR

This paper introduces a novel approach to teaching calculus by framing it through statistical concepts of mean, enabling understanding of calculus from data and sampling perspectives rather than solely from explicit formulas.

Contribution

It presents a statistics-based methodology for understanding calculus concepts, emphasizing averages and data interpretation to aid learners.

Findings

Defines integral via arithmetic mean and area interpretation

Introduces derivative as an average speed using graphic mean

Connects antiderivative and derivative through a unified operation

Abstract

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.