We investigate the number probability density function that characterizes subportions of a quantum many-body system with globally conserved number of particles. We put forward a linear fitting protocol capable of mapping out the ground-state phase diagram of the rich one-dimensional extended Bose-Hubbard model: The results are quantitatively comparable with more sophisticated traditional and machine learning techniques. We argue that the studied quantity should be considered among the most informative bipartite properties, being moreover readily accessible in atomic gases experiments.

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• Phase diagrams
• Phase transitions
• 1-dimensional systems
• Atomic systems
• Bose-Hubbard model
• Density matrix renormalization group
• Full counting statistics