The crystal structure of a material is essentially determined by the nature of its chemical bonding. Consequently, the atomic coordination intimately correlates with the degree of ionicity or covalency of the material. Based on this principle, materials with similar chemical compositions can be successfully categorized into different coordination groups. However, counterexamples recently emerged in complex ternary compounds. For instance, strongly covalent IB-IIIA-VIA₂ compounds, such as AgInS₂, prefer tetrahedrally coordinated structure (TCS), while strongly ionic IA-VA-VIA₂ compounds, such as NaBiS₂, would favor octahedrally coordinated structure (OCS). One naturally expects that IB-VA-VIA₂ compounds with intermediate ionicity or covalency, such as AgBiS₂, should then have a mix-coordinated structure (MCS) consisting of covalent AgS₄ tetrahedra and ionic BiS₆ octahedra. Surprisingly, only OCS was observed experimentally for AgBiS₂. To resolve this puzzle, we perform first-principles studies of the phase stabilities of ternary compounds at finite temperatures. We find that AgBiS₂ indeed prefers MCS at the ground state, in agreement with the typical expectation, but under experimental synthesis conditions disordered OCS becomes energetically more favorable because of its low mixing energy and high configurational entropy. This dataset includes structural information for the MCS and OCS configurations of ABX₂ compounds, along with the principal input data used for each calculation.