**ERIC Number:**EJ884060

**Record Type:**Journal

**Publication Date:**2010

**Pages:**9

**Abstractor:**As Provided

**Reference Count:**13

**ISBN:**N/A

**ISSN:**ISSN-0020-739X

The Statistics of a Function

Gordon, Sheldon P.; Gordon, Florence S.

International Journal of Mathematical Education in Science and Technology, v41 n3 p403-411 2010

One of the most important applications of the definite integral in a modern calculus course is the mean value of a function. Thus, if a function "f" is defined on an interval ["a", "b"], then the mean, or average value, of "f" is given by [image omitted]. In this note, we will investigate the meaning of other statistics associated with a function "f" on an interval, including the standard deviation, the skewness, the median and the shape of the distribution of values of the function about the mean, things that typically do not appear in introductory calculus courses, though they may arise in calculus-based statistics courses. In this way, we demonstrate how one can build much stronger interrelationships and connections between different branches of mathematics, something that is very important for students to see. (Contains 7 figures.)

Descriptors: Intervals, Statistics, Calculus, Mathematics Instruction, Mathematical Concepts, Teaching Methods, Correlation, Mathematical Formulas

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A