  The recovery of multivariate functions and estimating their integrals from
finitely many samples is one of the central tasks in modern approximation
theory. Marcinkiewicz--Zygmund inequalities provide answers to both the
recovery and the quadrature aspect. In this paper, we put ourselves on the
$q$-dimensional sphere $\mathbb{S}^q$, and investigate how well continuous
$L_p$-norms of polynomials $f$ of maximum degree $n$ on the sphere
$\mathbb{S}^q$ can be discretized by positively weighted $L_p$-sum of finitely
many samples, and discuss the relationship between the offset between the
continuous and discrete quantities, the number and distribution of the
(deterministic or randomly chosen) sample points $\xi_1,\ldots,\xi_N$ on
$\mathbb{S}^q$, the dimension $q$, and the polynomial degree $n$.
