Resulting probability density function (pdf) distributions ${\mathcal{P}}_d$ of the quantity d/a_bin (Eq. (1)), that is, the ratio of the projected separation of the binary d and its semi-major axis a_bin, for the stellar binary (shaded blue pdf) and planetary population (shaded orange pdf). The probability density value was obtained by binning the values of d/a_bin and normalising each bin by n_i/N_tot Δ x_i, where n_i is the number of counts in the bin, N_tot is the total number of elements in the sample, and Δ x is the bin size.