Final answer:
A quantitative variable is numeric, permits arithmetic calculations, and is assigned numerical values to facilitate these calculations. It is essential that the values of the variable can indeed vary, which excludes option (b).
Step-by-step explanation:
A quantitative variable can be defined as a variable that meets certain criteria, so when given multiple choices, we need to select all that apply. The correct definitions for a quantitative variable are as follows: (a) A variable that is numeric: This is true because quantitative variables consist of numerical measurements or counts.
(c) A variable on which arithmetic calculations can be performed: This is correct as quantitative variables can be added, subtracted, multiplied, or divided to provide meaningful results. (d) A variable that is assigned a value so that numeric operations can be performed on the assigned values: This is also a true statement, as quantitative variables are assigned numerical values for the purpose of conducting mathematical operations.
Option (b), 'A variable whose values do not change' is not a characteristic of a quantitative variable, as the definition of a variable is something that can vary or change.