Abstract: we study average of moments for event shapes in e^+ e^-→hadrons within the context of next to leading order (NLO) perturbative QCD prediction in dispersive model. Moments used in this article are <1-T>,〈ρ〉,〈B_T 〉 ,〈B_W 〉. We extract the coupling constant (α_s) in perturbative theory and α_0 in the non- perturbative theory using the dispersive model. By fitting the experimental data, we find the values of 〖 α〗_s (M_(Z^0 ))= 0.1171±0.00229 and α_0 (μ_I=2GeV)=0.5068±0.0440. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. We explain all these features in this paper.

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