Measured variance of the density PDF, i.e., diagonal elements of the covariance matrix, in sets 𝒜 for α = 0.5 and different prescription of the measured density. From left to right, raw density ρ_i, scaled density , and scaled density . The blue dots and solid lines are from the mean-field analytical expressions, and the large gold symbols are from the numerical simulations. The dashed black lines are what is expected from the large-scale leading contribution. The variance at cell scale is about 1.09, and the variance at sample scale, , is about 0.09.