# The Normal Curve and Outlier Detection

• Rand R. Wilcox

## Abstract

No doubt the reader is aware that the normal curve plays an integral role in applied research. Properties of this curve, which are routinely described in every introductory statistics course, make it extremely important and useful. However, in recent years, it has become clear that this curve can be a potential source for misleading—even erroneous—conclusions in our quest to understand data. This chapter summarizes some basic properties of the normal curve that play an integral role in conventional inferential methods. But this chapter also lays the groundwork for understanding how the normal curve can mislead. A specific example covered here is how the normal curve suggests a frequently employed method for detecting outliers that can be highly misleading in a variety of commonly occurring situations. This chapter also describes the central limit theorem, which is frequently invoked in an attempt to deal with nonnormal probability curves. Often the central limit theorem is taken to imply that with about twenty-five observations, practical problems due to nonnormality become negligible. There are several reasons why this is erroneous, one of which is given here. The illustrations in this chapter provide a glimpse of additional problems to be covered.

## Keywords

Central Limit Theorem Lower Quartile Outlier Detection Normal Curve Integral Role
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