Selected results of the simulations for bias of the estimators. Graphs shown here are for intermediate sample size (n = 100), and normally distributed contamination located at twice the distance between the true mode and the 99th percentile; see Supplementary Data for full results. Each column of graphs represents simulations for different original distributions: normal (left, a-d), lognormal (middle, e-h), and coarse (right, i-l). The top row (a, e, i) shows bias results for a comparison of three mode estimators with mean and median, all using 1000 replications. The lower three rows show bias results for comparisons between mode estimators with no bootstrapping (NBM, solid line), mode of 100 bootstrapped modes (BMO, dashed line), and mean of 100 bootstrapped modes (BME, dotted line), for HRM (b, g, l), RPM (c, h, n), and SPM (d, i, n); all using 100 simulation replications (100 bootstrap replications per simulation replication). In each case, the level of contamination applied to the original distribution ranged from zero to 40% (shown on X-axis). Bias is indicated in absolute units (Y-axis).