  Background and Objective: Histograms and Pearson's coefficient of variation
are among the most popular summary statistics. Researchers use histograms to
judge the shape of quantitative data distribution by visual inspection. The
coefficient of variation is taken as an estimator of relative variability of
these data. We explore properties of histograms and coefficient of variation by
examples in R, thus offering better alternatives: density plots and
Eisenhauer's relative dispersion coefficient. Methods: Hypothetical examples
developed in R are applied to create histograms and density plots, and to
compute coefficient of variation and relative dispersion coefficient. Results:
These hypothetical examples clearly show that these two traditional approaches
are flawed. Histograms do not necessarily reflect the distribution of
probabilities and the Pearson's coefficient of variation is not invariant with
linear transformations and is not a measure of relative variability, for it is
a ratio between a measure of absolute variability (standard deviation) and a
measure of central position (mean). Potential alternatives are explained and
applied for contrast. Conclusions: With the use of modern computers and R
language it is easy to apply density plots, which are able to approximate the
theoretical probability distribution. In addition, Eisenhauer's relative
dispersion coefficient is suggested as a suitable estimator of relative
variability, including sample size correction for lower and upper bounds.
