We present a phenomenological procedure of dealing with the COVID-19 (coronavirus disease 2019) data provided by government health agencies of 11 different countries. Usually, the exact or approximate solutions of susceptible-infected-recovered (or other) model(s) are obtained fitting the data by adjusting the time-independent parameters that are included in those models. Instead of that, in this work, we introduce dynamical parameters whose time-dependence may be phenomenologically obtained by adequately extrapolating a chosen subset of the daily provided data. This phenomenological approach works extremely well to properly adjust the number of infected (and removed) individuals in time for the countries we consider. Besides, it can handle the sub-epidemic events that some countries may experience. In this way, we obtain the evolution of the pandemic without using any a priori model based on differential equations.