Cumulative distribution functions for M₅₀₀ and Y₅₀₀, respectively. The top panel displays bins ranging from 10¹⁵ to 10¹⁴ M_⊙, with increments of ten, showing the random expectation of finding a cluster of a certain mass or higher within a sphere whose radius corresponds to the distance displayed on the x-axis. Simulated M₅₀₀ values, as estimated by SUBFIND, are represented in red. The blue data points represent the observed M₅₀₀ values obtained from clusters Planck signals, including their associated errors. In cases where SZ-derived M₅₀₀ values were unavailable, X-ray-derived M₅₀₀ values were used (indicated by square points). For cluster A347 X-ray-derived mass information was not available, thus we used the M₅₀₀ mass derived by converting the dynamical mass estimated by Tully. The observational uncertainties in the cluster’s position for Coma, A2734, AWM7, and Centaurus are represented by red lines, as an illustrative example of how such positional uncertainty can impact the results of the significance study (see Sect. 5.2 for a more comprehensive discussion). The bottom panel displays the cumulative distribution function for the SZ-derived signal in R₅₀₀. Simulated datapoint values where estimated using SMAC (Dolag et al. 2005a). The bins range from 3 × 10⁻⁶ to 3 × 10⁻⁴ Mpc², with increments of 2.