Data

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Discrete or Continuous VS Qualitative or Quantitative Data::

Very confusing for beginning students. 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, number of people, or number of chemical elements in a sample.
Usually a positive whole number is associated with each object. The integers (including the negatives and 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 that form a continuous set. Between any two real numbers there exists another real number. A curve (coming up) that is continuous can be traced with a pencil without lifting it off the paper.

Qualitative data is descriptive in nature. It has no numerical measurement associated with each data point. It is not metric in nature (measurable).
Examples are, chemical elements in cat food, your gender, your likes or dislikes, and so on.

Quantitative data is data that is measured. It is metric in nature. Any number of objects counted, your weight, your height, temperature, amount of certain chemicals in cat food and so on are examples.

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 and 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 and location.

Colors are tricky. If dealing with a finite number (countable) of colors, then we have a discrete set. This set is 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.

The levels of measurements are nominal, ordinal, interval, and ratio.
Nominal: Consists of names, gender, labels, or categories only. Data that cannot be arranged in any ordering scheme.(usually discrete data)
Ordinal: Data concerned with order or rank. Race results, letter grades in a course, college football rankings, and so on. The difference in data values is not measured.(usually discrete data).
Interval:(Metric data). Obtained from the measurement of quantities such as temperature and time. (usually continuous data). Uses a constant scale with differences having meaning but ratios do not (since there is no natural zero). (absence of the quantity). For example, the difference of 80 degrees & 40 degrees can be measured but you can not conclude that the ratio of 80/40=2 means it's twice as hot.
Ratio: Metric data uses a continuous, constant scale. Both differences and ratios can be measured. There is a natural zero. Examples would be the measurements of height and weight.

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 course 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.