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an independent variable
A categorical variable (also known as a discrete variable) is one whose range is countable; e.g. the variable answ has values [yes, no, not sure]. answ is a categorical variable with range 3.A continuous variable is one which is not categorical; e.g. weight is a continuous variable which can take any value between 0 and 1000 kg (say) for a human being.
Some functions put a limit on the range; for example. y=x2 produces only nonnegative numbers. The sine and cosine functions limit the range between 1 and -1.
The range, in one sense, is defined as the difference between the highest and lowest numbers, which in this instance is from 167 to 579. In function theory, the data set itself could be the range, if these are the only values of the independent variable for which the dependent variable is defined.
When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").