  Dwarf spheroidal galaxies (dSphs) are the most compact dark matter-dominated
objects observed so far. The Pauli exclusion principle limits the number of
fermionic dark matter particles that can compose a dSph halo. This results in a
well-known lower bound on their particle mass. So far, such bounds were
obtained from the analysis of individual dSphs. In this paper, we model dark
matter halo density profiles via the semi-analytical approach and analyse the
data from eight `classical' dSphs assuming the same mass of dark matter fermion
in each object. First, we find out that modelling of Carina dSph results in a
much worse fitting quality compared to the other seven objects. From the
combined analysis of the kinematic data of the remaining seven `classical'
dSphs, we obtain a new $2\sigma$ lower bound of $m\gtrsim 190$ eV on the dark
matter fermion mass. In addition, by combining a sub-sample of four dSphs --
Draco, Fornax, Leo I and Sculptor -- we conclude that 220 eV fermionic dark
matter appears to be preferred over the standard CDM at about 2$\sigma$ level.
However, this result becomes insignificant if all seven objects are included in
the analysis. Future improvement of the obtained bound requires more detailed
data, both from `classical' and ultra-faint dSphs.
