Abundance distributions of our complete (AGB + RGB) sample. Left: [Na/H]_NLTE−T_eff; middle: [Na/Fe i]_NLTE−T_eff; right: [Na_NLTE/Fe ii]−T_eff. Symbols are the same as in Fig. 2. The horizontal dash-dotted lines mark the critical values distinguishing the 1P and 2P stars following Carretta et al. (2009b) criteria (see the text). The typical error bars are shown at the right-bottom corner of each panel (considering the similarity of the errors of the GIRAFFE and UVES samples and the clarity of the figure, we only show the error bars for the GIRAFFE sample which is the largest sample here).