It is more the other way around, in that the question is better asked as, "How many fish are categorized as vertebrates". The answer to that question would be "almost all fish are vertebrates". Because most all fish do have vertebral columns (backbones/spines), internal skeletons, brains and central nervous systems located in craniums (heads) with sensory organs at the fore sections of their bodies. There are some non-bony fish, like hagfish, that are classified sometimes as invertebrates by some, but more often are classified as vertebrates even though they do not have backbones. They could technically be invertebrates. But they have the other characteristics of vertebrates and a very close genetic make up to lampreys, that are vertebrates.