The “Calculus” of Moving Averages

Abstract

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The article: (1) shows how to calculate the moving averages for a set of data; (2) discusses the effect of the length of the moving average cycle on the sequence of values generated; (3) discusses the mathematical properties of the moving average as a mathematical function/operator; (4) addresses the problem of how to retrieve the underlying sequence of data values from the known sequence of values of the moving averages; and (5) discusses the significance of the moving averages in the sense of smoothing out the original data to better identify the pattern in that data.

KEYWORDS:

• Moving averages
• fitting functions to data
• inverse problem with moving averages
• moving averages of moving averages

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Sheldon P. Gordon

Shelly Gordon is SUNY Distinguished Teaching Professor of Mathematics at Farmingdale State College in New York, USA. He has been deeply involved in efforts to revitalize the undergraduate mathematics curriculum at all levels ranging from algebra, precalculus, calculus, differential equations, and statistics and probability, particularly from the perspective of the use of technology to enhance student understanding of mathematical concepts and methods. Shelly has authored about 225 papers, a dozen textbooks and monograph volumes, and hundreds of software programs for mathematics education that bring the concepts and methods alive for students via dynamic graphical and numerical perspectives.

Florence S. Gordon

Flo Gordon is Professor of Mathematics (emeritus) at New York Institute of Technology in Old Westbury, New York, USA. She is a co-author of Functioning in the Real World and Contemporary Statistics: A Computer Approach and co-editor of the MAA volumes, Statistics for the Twenty First Century and A Fresh Start for Collegiate Mathematics: Rethinking the Courses Below Calculus. She is also the author of about 80 papers on mathematics and statistics education. She has been very involved in efforts to improve the teaching of mathematics at all levels, with special emphasis on statistics and precalculus education.