#### Publication Date

11-2015

#### Abstract

In statistical analysis, we usually use the observed sample values x_{1}, ..., x_{n} to compute the values of several statistics v(x_{1}, ..., x_{n}) -- such as sample mean, sample variance, etc. The usual formulas for these statistics implicitly assume that we know the exact values x_{1}, ..., x_{n}. In practice, the sample values X_{1}, ..., X_{n} come from measurements and are, thus, only approximations to the actual (unknown) values x_{1}, ..., x_{n} of the corresponding quantity. Often, the only information that we have about each measurement error Δ x_{i} = X_{i} − x_{i} is the upper bound Δ_{i} on the measurement error: |Δ x_{i}| ≤ Δ_{i}. In this case, the only information about each actual value x_{i} is that it belongs to the interval [X_{i} − Δ_{i}, X_{i} + Δ_{i}]. It is therefore desirable to compute the range of each given statistic v(x_{1}, ..., x_{n}) over these intervals. It is known that often, estimating the range of a robust statistic (e.g., median) is computationally easier than estimating the range of its traditional equivalent (e.g., mean). In this paper, we provide a qualitative explanation for this phenomenon.

## Comments

Technical Report: UTEP-CS-15-87

To appear in

Journal of Innovative Technology and Education