ML-MS binary fraction vs. the cluster age (upper left), central density (upper right), [Fe/H] (lower left), and total cluster mass (lower right). The closed circles are the uncorrected binary fractions (f _b,i) and the open circles are the corrected binary fractions (f _b,c). The colors correspond to the cluster in the same manner as previous figures. In the upper-left panel, the black line denotes the field binary fraction for solar-type stars, the black dashed line denotes the field total multiplicity fraction, and the gray region marks the uncertainty of these binary fractions.