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Star Library: What Makes the Standard Deviation Larger or Smaller?
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The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the Š—“variationŠ— in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation.

Subject:
Mathematics
Statistics and Probability
Material Type:
Activity/Lab
Provider:
Consortium for the Advancement of Undergraduate Statistics Education
Provider Set:
Causeweb.org
Author:
delMas, Robert C.
Date Added:
02/16/2011