Final answer:
The statement is true as metals exhibit a wider range of properties such as malleability, ductility, and conductivity compared to the more limited diversity of nonmetals, which are typically dull, brittle, and poor conductors.
Step-by-step explanation:
The statement "The variation in properties among metals is greater than the variation in properties among nonmetals" is generally considered true. Metals, which make up the majority of elements on the periodic table, show a broad range of physical characteristics such as malleability, ductility, conductivity, and appearance. For instance, metals like sodium and potassium are quite soft, while others like iron are very hard. Moreover, metals can be shiny and silvery while still varying significantly in color and luster. In contrast, nonmetals are more limited in this diversity, often being dull, brittle in solid form, and poor conductors of heat and electricity.
While there are exceptions and some overlap with metalloids, the general tendency is for metals to lose electrons and form cations due to their low electronegativity, whereas nonmetals tend to gain electrons becoming anions, indicated by their higher electronegativity. The properties of solid nonmetals, such as brittleness and poor conductivity, further emphasise the broader variation seen in metals when compared to nonmetals.