Standard deviation of the logarithm of chi-square distributed white noise rebinned on the annulus with the radius of k_pix pixels, σ^scat, is plotted against the square-root of the pixel number on the annulus after rebinning, , at three k_pix shown with different symbols in different colors. In the case of n_pix ≪ 2πk_pix, σ^scat = σ_α(α = 1.5), which is shown with the dotted lines, is a valid approximation, while in the limit of n_pix ≳ 2πk_pix, σ^scat deviates from σ_α and approaches a constant of 2/3.