  The classical form of Gr\"{u}ss' inequality was first published by G.
Gr\"{u}ss in 1935 and gives an estimate of the difference between the integral
of the product and the product of the integrals of two functions. After that
many variants of this inequality appeared in the literature. The aim of this
paper is to consider some Chebyshev-Gr\"{u}ss-type inequalities and apply them
to Bernstein-Euler-Jacobi (BEJ) operators of first and second kind. First and
second moments of the operators are used to explain the situation.
