Comparison of observed mid-infrared (MIR) H i line ratios with model predictions from KF11. Top panels show theoretical line ratio curves as a function of hydrogen density (n_H) for different gas temperatures, with coloured curves corresponding to temperatures ranging from 3750 K to 15 000 K. Vertical lines represent the observed median (dash-dotted), 25th percentile (dotted), and 75th percentile (dashed) values for each ratio. The bottom panels display horizontal violin plots of the observed line ratios from our sample, with circles indicating individual ratio values. In each of the top panels, the shaded regions show the inferred range of n_H values for three different temperature grids, with the colours corresponding to the respective temperatures (green for T=7500K, red for T=8750, and brown for T=12 500 K). These comparisons demonstrate the sensitivity of certain MIR H i line ratios (e.g. H i (10–6)/H i (7–6), H i (9–7)/H i (10–7)) to hydrogen densities ≳ 10^10.2 cm⁻³.