~Discrete Data has "gaps" between data points. There are no data points in these gaps. Examples are: a given number of objects being counted such as a given number of bottles, or, number of people, or, number of chemical elements in a sample. Usually a positive whole number is associated with each object. The integers (including negative & zero) form a discrete set since there are no integers between any two consecutive integers.

~Continuous data has no "gaps". Between any two data points there will exist another data point. Continuous implies no breaks or holes. The real number line is an example of a set of numbers that form a continuous set. Between any two real numbers there exists another real number. A curve that is continuous can be traced with a pencil without lifting it off the paper.

~Discrete data could be quantitative. For example, the number of fish you catch on a camping trip. Usually, discrete data is qualitative more often. When a measurement is involved, it becomes quantitative. Phone numbers & addresses form discrete data sets which are qualitative in nature since, without any added definitions, they do not measure anything. They are used for identification purposes & location.

~Colors are tricky. If dealing with a finite (set number) of colors, then we have a discrete set & this set is usually qualitative in nature (not measured). However, if dealing with the visible spectrum, then the colors are continuous (determined by their wavelengths) and this set would be quantitative in nature. So, be aware of these situations. A bit on the tricky side.

~Unfortunately, when one looks at the levels of measurements (nominal, ordinal, interval, & ratio), the first is really data that is not measured, so it will be qualitative in nature. In my opinion, the word measurement should not be used in a title unless a measurement can be performed. For example, male or female is an example of nominal data, but qualitative (not measured). The number of males or females would be quantitative.

~Additional comments: Scientists usually separate data (collected pieces of information) into two main types:

a) Categorical or Qualitative (data points are placed in groups)

Data in this group may contain numbers and may be ordinal in nature (i.e., house numbers), but performing mathematical operations with these numbers (adding, dividing, etc.) make no sense. Most of the time, the data sections describe a characteristic of that group (i.e., male, female, or rating scales giving different levels of satisfaction). In many cases, numbers are used for labeling in each section (i.e., 1=male, 2=female). Even though this is nominal data, it can be Ordinal (the numbers are placed in some order) (i.e., house numbers).

b) Metric or Quantitative (data points that give measure, i.e., “how much”)

Data of this type is mostly used in scientific fields. It may be Ordinal, as well, along with the Ratio & Interval types.

Scientists most likely use the terms Discrete & Continuous when referring to Quantitative data.

For chemistry majors, a couse in Qualitative Analysis will deal with the identification of the elements in a given sample, while a separate course in Quantitative Analysis, deals with the exact amount of each element detected. I've taken both courses while in college.