Can there be qualitative data that has an infinite number of classes? | Doubt | Mistakes | Week 4 / Descriptive Statistics / Different types of data

The lecture defines Qualitative Data as
" Qualitative or categorical attributes are those which describe the object under consideration using a finite set of discrete classes"

Coming to my question, can there be qualitative data with an infinite number of classes?
Example: Name of a person. Assuming that a person’s name can be arbitrarily long, we can have an infinite number of classes for it.

Also, the video says the following about Discrete Attribute
"Discrete attributes are those quantitative attributes which can take on only a finite number of numerical values"

But this definition is thoroughly wrong, as there are a countably infinite number of integers.

Also, it says continuous attributes “refer to quantitative attributes which can take on fractional values (Real Numbers)”, but Real Numbers also contain irrational numbers, which are not fractions.

Please let me know if any of the points I have made above are incorrect.

I understand that definitions have to be simplified to be inclusive of people with varying backgrounds, but some of these are very misleading and factually wrong. Many of us are expecting this course to be mathematically rigorous, so I think we should be kept in mind as well when simplifying definitions.

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Seems you have mis-understood how the Qualitative Data is used for analysis. “Qualitative” data describes qualities or characteristics. They are most of the times complex to process in raw form (Say they might be bag of words collected in a Survey) and they need to be processed sometimes applying a process called coding. This Coding process will eventually convert the raw complex data into finite classes for answering the most pertinent question. So in your case, the coding will be to categorize the names into classes such as A-C , C-F, F-J etc… then you will end up with finite classes to answer any relevant questions you may have.

The way you understood the definition of Qualitative and Quantitative is little different what the instructor is intending to explain. Basically, not going by the jargon, first understand that the Qualitative of Quantitative are the types of attributes and not the data contained in them. Therefore, qualitative attributes are something which label the object and Quantitative attributes are something which measures the object. Moreover, if you agree, these attributes can be classified as per the statistics operations performed on them. Like calculating frequency of a label is still logical but calculating average of a label attribute is illogical.
Hope now it make sense as which category does the name of a person comes into. It is off course a label. There is a sense in calculating the frequency of a particular name but average of this attribute cannot be calculated. Moreover, it is not a measure of any person. Therefore, one side you are correct that there can be infinite no. of names but eventually they can be divided into several finite classes.

Hope that helps!!!


Coming to your second question about the Discrete attributes. Now discrete attributes are something which takes the finite value for an object but the no. of values of that attribute can be infinite. Like the no. of people visiting the bank or a retail shop in a day. This will be a finite value say, 30 people or 40 people in a day, but the range of values can be infinite starting 0 to infinity(hypothetically).

Regarding Quantitative attribute, here the instructor is referring to the continuous data type which can contain fractions also.



Just to add to what @Pankaj_Rana has explained,
One can think discrete attribute as for a given range, it can only take finite number of possible values say between [1,10] you have only 10 values not more not less, whereas in the continuous case you all have infinite possibility between [1,10] like 1.11, 1.1111, 1.1111 it goes on infinitely.
The names discrete and continuous is intended to capture this nature.

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