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Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="double-struck">R</mi> <msub> <mo>&#215;</mo> <mi mathvariant="fraktur">f</mi> </msub> <msub> <mi>N</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> <msub> <mo>&#215;</mo> <mi mathvariant="fraktur">f</mi> </msub> <mi mathvariant="double-struck">R</mi> </mrow> </semantics> </math> </inline-formula>. Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen&#8217;s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi&#8722;Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.