  We propose a complementary and fast approach to study galaxy rotation curves
directly from the sample data, instead of individual fits. With this approach,
some relevant tests can be done analytically. It is based on a dimensionless
difference between the observational rotation curve and the expected one from
the baryonic matter ($\delta V^2$) as a function of the normalized radius $r_n$
(i.e., for all galaxies, $0 < r_n < 1$). Using 153 galaxies from the SPARC
galaxy sample, we find the observational distribution of $\delta V^2$.
Considering radii with $0.2 < r_n < 0.9$, most of the SPARC data are close to
the curve $\delta V^2 = r_n^{0.42}$, and about $95\%$ of the SPARC data is
between the curves $\delta V^2 = r_n^{2.2}$ and $\delta V^2 = 2 r_n^{0.38} -
r_n^{1.9} $. We consider three well known dark matter halo models (NFW, Burkert
and DC14), a simple dark matter rotation curve profile for the purpose of model
comparison (Arctan$_\alpha$) and one modified gravity model without dark matter
(MOND). By comparing the observational data distribution with the
model-inferred data, we confirm that the NFW halo lacks the necessary diversity
to reproduce several observed rotation curves, while Burkert and DC14 models
have better concordance with observational data. The lowest $\delta V^2$ curves
that can be found from NFW are linear on the normalized radius (i.e., $\delta
V^2_{NFW} = r_n$), while for Burkert $\delta V^2_{Bur} = r_n^2$ (this result is
independent of the halo density parameter, i.e., $\rho_{c}$ or $\rho_{s}$).
MOND only covers the very central region of the observed distribution, hence it
also lacks the necessary diversity, which in turn is related to larger $\chi^2$
values. In a second paper, the method will be extended to consider other
classes of modified gravity models.
