Everything can be quantified. Some problems are impossible to quantify. Structured data are objective. Qualitative data are subjective. Etc. etc. Nope, that's wrong.
Qualitative data usually looks like a bunch of words while its quantitative brethren like numbers in a spreadsheet. But they're not fundamentally different.
As professor Trochim ↗︎ writes:
All qualitative data can be coded quantitatively
All quantitative data is based on qualitative judgment
You can assign meaningful numerical value to anything qualitative. And then manipulate this data in the beneficial quantitative ways. Conversely, numbers mean something and what they mean often rests on many apriori qualitative judgements.
Old-school qualitative-oriented people believe that whatever it is you want to understand, you need to view the problem in its context. But you will hear "context is critical" mantra also from great data practitioners like Giorgia Lupi or Alberto Cairo.
The traditional view postulates that quant and qual data stem from fundamentally different way of looking at the world.
See, for example, this note in the wonderful garden called Moby Diction:
Whereas quantitative researches seek precision and scale, qualitative researchers seek context and human empathy. Quantitative researchers want to know what happened, and how frequently. Qualitative researchers want to know how and why the thing occurred.
Quantitative research, then, looks to explain reality as it is; qualitative research looks to explain reality as it is interpreted.
But even Moby Diction in other notes concedes the distiction here maybe more of an emphasis than ontology and epistemiology:
This isn't to say that quantitative analysis is not without merit; however, it must be undertaken with the understanding that its emphasis on scale and causation may come at the cost of coherence and focus.