Let G be a finite group, we define the average codegree of the irreducible characters of G as acod (G) = 1 | Irr (G) | ∑ χ ∈ Irr (G) cod (χ) , where cod (χ) = | G : ker χ | χ (1) . We prove that if G is non-solvable, then acod (G) ≥ 6 8 / 5 , and the equality holds if and only if G ≅ A 5 . Also, we show that if G is non-supersolvable, then acod (G) ≥ 1 1 / 4 , and the equality holds if and only if G ≅ A 4 . In addition, we obtain that if p is the smallest prime divisor of | G | , then acod (G) < p if and only if G is an elementary abelian p -group. [ABSTRACT FROM AUTHOR]