The optical extinction spectra of single silver nanoparticles coated with a silica shell were investigated in the size range 10-50 nm. Measurements were performed using the spatial modulation spectroscopy technique which permits independent determination of both the size of the metal nanoparticle under study and the width of its localized surface plasmon resonance (LSPR). These parameters can thus be directly correlated at a single particle level for the first time. The results show a linear increase of the width of the LSPR with the inverse diameter in the small size regime (less than 25 nm). For these nanoparticles of well-controlled environment, this can be ascribed to quantum confinement of electrons or, classically, to increase of the electron surface scattering processes. The impact of this effect was measured quantitatively and compared to the predictions by theoretical models.