these fits, we now trim likely outliers by application of a 2-$\sigma$ clipping procedure, for example:

$$\rm <[Fe/H]> - 2\sigma_{\rm [Fe/H]} \leq \rm [Fe/H]_{\star} \leq
\rm<[Fe/H]> + 2\sigma_{\rm [Fe/H]} \label{eq6}$$

$$\rm <RV> - 2\sigma_{\rm RV} \leq \rm RV_{\star} \leq \rm<RV> +
2\sigma_{\rm RV} \label{eq7}$$

In the above, \[Fe/H\]$_{\star}$ and RV$_{\star}$ correspond to the values of these parameters for each star under consideration. The stars surviving both of these clips are considered true cluster members for the purpose of this study. Note that at no point have we considered the external “known” values of \[Fe/H\] and RV for the clusters as a whole.

Based on the application of these membership cuts, we now have a total of 169 stars identified as true members of M 13, 63 stars as true members of M 15, 9 stars as true members of M 2, 195 stars as true members of NGC 2420, and 51 stars as true members of M 67. The distribution of \[Fe/H\] and RV for the surviving members of M 13 are shown as green histograms in the left and right panels of Figure 5, respectively. Similar plots for M 15, M 2, NGC 2420, and M 67 are shown 