What does measurement level have to do with discrete vs. continuous?
Measurement level has nothing to do with discrete vs. continuous variables. The distinction between discrete and continuous random variables is commonly used in statistical theory, but that distinction is rarely of importance in practice. A continuous random variable has a continuous cumulative distribution function. A discrete random variable has a stepwise-constant cumulative distribution function. A discrete random variable can take only a finite number of distinct values in any finite interval. There exist random variables that are neither continuous nor discrete; for example, if Z is a standard normal random variable and Y=max(0,Z), then Y is neither continuous nor discrete, but has characteristics of both. While measurements are always discrete due to finite precision, attributes can be conceptually either discrete or continuous regardless of measurement level. Temperature is usually regarded as a continuous attribute, so temperature measurement to the nearest degree Kelvin is a
