I wrote this for graduate school in 2013 and it was one of the more popular posts on my old blog so I figured I’d repost it here.
2019 update: I've moved this over from Medium as it was my most popular post there. Two of the original references are dead links, so I have removed them.
Qualitative data and quantitative data refer to different kinds of data and originate from statistics. Both of these types of data can be subjective or objective. Neither is exclusive to the other.
Subjectivity is used to refer to the condition of being a subject; the quality of a subject’s perspective, experiences, feelings, beliefs, and desires.  Subjective information is one person’s opinion.
Objectivity is the idea that scientists, in attempting to uncover truths about the natural world, must aspire to eliminate personal biases, a priori commitments, emotional involvement, etc. 
Quantitative data comes from the word quantity, indicating amount. It is a measure of something, number, size, etc.
Qualitative data comes from the word quality. Indicates a description of something. It focuses on the subject’s properties, characteristics, features, etc.
Objective, Quantitative: “The chip speed of my computer is 2 GHz” Subjective, Quantitative: “On a scale of 1–10, my computer scores 7 in terms of its ease of use”
Objective, Qualitative: “Yes, I own a computer”
Subjective, Qualitative: “I think computers are too expensive”