What is the difference between categorical (qualitative) data and numerical (quantitative) data?

Actually there are three main types of data.

Qualitative or categorical data have no logical order, and can't be translated into a numerical value. Eye colour is an example, because 'brown' is not higher or lower than 'blue'.

Quantitative or numerical data are numbers, and that way they 'impose' an order. Examples are age, height, weight.But watch it! Not all numerical data is quantitative. One example of an exception is the security code on your credit card -- there is no logical order between them.

Class data is considered the third type. They are not continuous, like quantitative data, but they can be ordered. Most known example are letter grades for tests.

Use: Quantitative data can be used with all three centre measures (mean, median and mode) and all spread measures. Class data can be used with median and mode Qualitative data can only be used with mode.