  We present a new parametrization of the cosmic-ray flux and its mass
composition over an energy range from 10 GeV to $10^{11}$ GeV. Our approach is
data-driven and relies on theoretical assumptions as little as possible. We
combine measurements of the flux of individual elements from high-precision
satellites and balloon experiments with indirect measurements of mass groups
from the leading air shower experiments. To our knowledge, we provide the first
fit of this kind that consistently takes both statistical and systematic
uncertainties into account. The uncertainty on the energy scales of individual
experiments is handled explicitly in our mathematical approach. Part of our
results is a common energy scale and adjustment factors for the energy scales
of the participating experiments. Our fit has a reduced $\chi^2$-value of 0.5,
showing that experimental data are in good agreement, if systematic
uncertainties are considered. Our model may serve as a world-average of the
measured fluxes for individual elements from proton to iron from 10 GeV to
$10^{11}$ GeV. It is useful as an input for simulations or theoretical
computations based on cosmic rays. The experimental uncertainties of the input
data are captured in a covariance matrix, which can be propagated into derived
quantities.
