EXPLORING STUDENTS’
CONCEPTIONS OF

**THE STANDARD DEVIATION**

ROBERT DELMAS

University of Minnesota

delma001@umn.edu

YAN LIU

Vanderbilt University

yan.liu@vanderbilt.edu

SUMMARY

This study investigated introductory statistics students’ conceptual understanding of the standard deviation. A computer environment was designed to promote students’ ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an interview divided into two primary phases, an exploration phase where students rearranged histogram bars to produce the largest and smallest standard deviation, and a testing phase where students compared the sizes of the standard deviation of two distributions. Analysis of data revealed conceptions and strategies that students used to construct their arrangements and make comparisons. In general, students moved from simple, one-dimensional understandings of the standard deviation that did not consider variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean. Discussions of the results and implications for instruction and further research are presented.

** Keywords**: Standard deviation; Variability; Conceptions;
Strategies; Interviews

**__________________________**

*Statistics Education Research
Journal, 4(1), 55-82, http://www.stat.auckland.ac.nz/serj*

*Ó International
Association for Statistical Education (IASE/ISI), May, 2005*

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ROBERT DELMAS

University of Minnesota

354 Appleby Hall

128 Pleasant Street SE

Minneapolis, MN 55455

USA