In the present work, we propose to investigate statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability by means of deferred N örlund and deferred Riesz mean. We discuss some fundamental theorems connecting these concepts with examples. As an application to our newly formed sequences, we introduce Korovkin-type approximation theorems with relevant example for positive linear operators by using Meyer-K önig and Zeller operators to exhibit the effectiveness of our findings.