Assume a large microscopic internal bonding chemical structure of a substance designed like a Petersen graph where electrons are the vertices and edges representing the bonding energy levels in between them. For large structures, it is difficult to find out the average level of bonding energy between any pair of electron-proton microscopic structures. For a chemical scientist, it is a difficulty and a challenge both to find out what is the average amount of energy bounded between any subsequent pair of electron-proton bi-valent bond, trivalent bond, or tetravalent bond. This paper presents a sample-based estimation methodology for estimating the bonding energy mean value. A node-sampling procedure is proposed whose bias, mean-squared errors and other properties are derived. Results are supported by empirical studies. Findings are compared with particular cases and confidence intervals are used as a basic tool of comparison for robustness purposes.