Maximum Z Scores and Outliers

1988/02/01 by Ronald E. Shiffler · 237 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Bounded function #Combinatorics #Data set #Magnitude (astronomy) #Mathematical analysis #Mathematics #Multi-Criteria Decision Making #Outlier #Physics #Standard deviation #Statistics #Value (mathematics)

paper · doi:10.1080/00031305.1988.10475530

published in The American Statistician 42(1), 79-80 (Taylor & Francis)

openalex publication_date 1988/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

The magnitude of Z(n), the Z score associated with the largest value of X in a data set of size n, is shown to be bounded above by (n — 1)/√n. As a result, outliers defined as values exceeding four standard deviations from the mean cannot exist for small data sets.

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