Statistics: Why are school grades qualitative variable?

Question

I am struggling to understand, why in descriptive statistics we say that school grades are a qualitative and not quantitative variable? I can understand why color of the hair is qualitative, but grades are numerical...

Answer 1

It depends where you live. For example, in Greece grades are in a scale 1-20, therefore quantitative.But in the U.S. for example they have A,B,C.. so you could say that there the grades is a qualitative variable.

Answer 2

A finer categorization of the "level of data" is surely "nominal scaled", "ordinal scaled", "interval scaled" and "ratio scaled" (see more about this in wikipedia).

"nominal" are data for instance from your example of color of hair, or telephone numbers or ICD-codes or many labelings ...
"interval" are data like temperature, for instance degree of Celsius or of Fahrenheit, which we give numerical values on the scale of real numbers, and "ratio" if they have a zero which are inherent/relevant with the meaning of the measure, such that relations as "double" or "half" make sense.

With grades in school it is between those concepts; while they are usually no measure related to the natural or real numbers, they still have an order: level "A" is better than "B" and that is better than "C" or so -and what is precisely what we want usually with such grades-, but what "nominal" data don't have. So the term "ordinal scale" has been introduced.

There is a lot more to say about, but I think wikipedia is a good-enough source for the beginning.