The measurable variable is the variable that is measured in an experiment. It changes depending on the adjustment of the independent variable.
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One way is to check whether the pre-image of the product is sigma-algebra. Please list an example to clarify your question.
Yes.
Measurable data is data that can be measure by a quantity. Measurable data is also known as quantitative data.
The data collected does not have to be measurable.
A concept is an idea or an abstraction that stands for something. A concept becomes a variable when it is made operational or when it can be counted, categorized, or observed. For example, job satisfaction is a concept, but, it becomes a variable when a definition is it attached to it that makes it measurable. You may ask a married person, "how satisfied are you with your job?" If you attach levels of satisfaction to it, then it becomes a variable. All variables are concepts when you can measure the concept. However, not all concepts can be variables. A concept that is not a variable is a concept that is not measurable.