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In many sources, for example here data is classified as being qualitative (categorical) and quantitative (numerical). Where numerical data can be continuous or discrete, and discrete can be finite or infinite.

I want to establish if a numerical, discrete and finite data can also be treated as categorical data.

I know that it depends on 'the meaning' of the data and requires some common sense analysis but I want to establish if the following statement is always true:

"Numerical, discrete and finite data can also be a categorical data"

In the classification of data the numerical data is said to have 'mathematical meaning as a measure of something'. But 'technically', without assessing the meaning of the data, it does also make them capable of being a categorical data (ordinal or not), if we strip it from mathematical meaning.

Example can be a following array of items:

Energy

15
15
20
25
25

Every observation has 'Energy' characteristic it can be treated as mathematical discrete and finite numerical value which can be a measurement of energy an item has. But also it can be treated as a category: two items are in 15 category, one in category 20 and two in category 25.

Thanks for confirming this.

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I would separate value with representation in this case.

Energy as you mentioned, in the real world, holds a very continuous value. However, we may choose (for various reasons) to represent this value in different forms.

We can take values as they are (15.21252, 23.76535), we can round them into integers (15, 24), we can even decide to represent this data by clusters ("UNDER 20", "OVER 20").

Technically, all data can be represented as categorical data, we need to consider what value does this data represent, and what are we losing/gaining from using different representations.

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    $\begingroup$ thanks for the answer, value vs representation separation is helping indeed. I was referring to Energy not as physical measure but just as example, ie. in a game a number of opponents can have 'energy' level, expressed simply in 'units'. Anyway this concept helps. I understand that by 'value' you mean the data provided, and representation depends on our needs/purpose. $\endgroup$ – mtx Feb 4 at 14:17

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