CDF of the median obliquity, θ₅₀, from our hierarchical Bayesian analysis. The upper horizontal axis translates θ₅₀ into the concentration κ of the Fisher distribution. Black curves are posteriors based on the full sample, assuming all planets have f  =  0.1, comparable to Saturn. The blue curve is the posterior assuming f  =  0.06, comparable to Jupiter. The red curve is based on half the planets; weaker constraints are obtained, reflecting the fact that useful information is distributed across all systems. The green curve shows the posterior assuming f is assigned via Equation (12). Assuming f  =  0.1 or f  =  0.06, the data imply θ₅₀  <  12^∘ or θ₅₀  <  66^∘, respectively, at 90% confidence.