Chapter 46: Sample Variance and Population Variance: Situation 40 From the MACMTL-CPTM Situations Project
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Published:2015
Ken Montgomery, Sarah Donaldson, 2015. "Sample Variance and Population Variance: Situation 40 From the MACMTL-CPTM Situations Project", Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations, M. Kathleen Heid, Patricia S. Wilson, Glendon W. Blume
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A student in a statistics class had observed that the definition of sample variance (s2) resembles the average of the squares of the deviations from the mean of the data set.
Yet, these squared deviations are summed and then divided by (n – 1). “Why,” asked the student, “do you not divide by n ? Is this an actual mean or some sort of 'pseudomean'?”
The concept in statistics known as variance is closely related to standard deviation: Both indicate the spread of the data distribution about the mean. In fact, the standard deviation is simply the principal square root of the variance. There are a number of reasons why the variance is calculated the way it is. As the formula for sample variance shows, the sum of the squared deviations is divided by n – 1. The following Foci are investigations of reasons why division by n – 1, rather than division by n , is necessary to calculate the sample variance. For discussion of division by n – 1 and the concept of variability, see references such as Agresti and Franklin (2007); Freund (1992); Mendenhall, Beaver, and Beaver (2005); Peck, Gould, and Miller (2013); and Shaughnessy and Chance (2005).
