There are two types of data: things that we measure and things that we count. Continuous data is data that can be derived from measuring things. Continuous data can be defined as any data that is measured by a measuring device (e.g. stopwatch, scale, tape measures), and can take on any value within a continuum. It can also be logically divided. A tape measure can be used to measure your height. It can take any value within a continuum and can be subdivided into inches, feet, one-quarter inch, one-eighth inch, etc. Because of the precision of the logical subdivisions of values, continuous data is valuable. Attribute data, also known as discrete data, is information that can be counted. The data can then be refined to discrete numeric and discrete attribute. A few examples of discrete numerical data are the number errors in your invoice, rejected parts on your manufacturing lines, and the number people waiting on hold for your customer service representative to pick up the telephone.
The data that is not part of a set of attributes is slightly different. This data assigns a numerical value to a qualitative characteristic. These qualitative characteristics can be referred to as discrete ordinal data if they have a logical arrangement. An Likert scale is an example. We can choose from the following attributes: Neutral, Moderately agree or Strongly disagree. We would assign them a numerical value such as 5, 4, 3, 2 or 1. Then, we can count each number.
You can also have discrete attributes data that are not ordered. We can, for example, define our attributes in terms if the products we are referring to. One glass company might categorize its products in three categories: laminated glass (tempered glass), insulated glass (insulated glass), and coated glass. They are all different and there is no logical order. They can be assigned a numerical code and I can count how many.
What does it matter what type of data you have? The type of data that we have determines the type and type of analytical tools we use. We prefer continuous data, which is more robust and flexible and allows for greater data refinement. Many people feel tempted to gather continuous data and then transform it into discrete or attribute data. You could, for example, collect delivery times for each order. This would be continuous data. You then transformed it into binary attribute data, consisting of on/not on time. This results in the loss of a lot information that could be used to analyze that process.