Illustration of our method using a skew-normal distribution to average different physical quantities at a given redshift, for many merger trees. (top) Distribution of the temperature values from all merger trees at redshift z = 0.75. The blue line represents the skew-normal distribution used to fit the data. The dashed line and the blue-shaded line, respectively, are the distribution’s median (that is used as an estimator for the average of all curves) and its corresponding 90% confidence interval. (middle) Distribution of magnetic field values at this same redshift. The two dashed black lines indicate the region that is fit with the skew-normal distribution. (bottom) Fitting within the region in the middle panel. Those three panels were computed with Re_eff Model L, for log₁₀(B₀ [G]) = −20, α₀ = 20, and z_start = 1.5.