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A random variable $X$ is called continuous if its set of possible values is uncountable, and the chance that it takes any particular value is zero ($\text{P}(X = x) = 0$ for every real number $x$). A random variable is continuous if and only if its cumulative probability distribution function is a continuous function.

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What type of variable is file size?

Weight and height are also continuous, even if in practice they can only be measured as units of grams (g) or millimeters (mm). It's more related to the nature of the variable, not as much to the part …
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