What is a continuous variable in statistics? Continuous variables can be split into three categories according to statements over here: http://www.unesco.org/webworld/idams/advguide/Chapt1_3.htm. One category is Interval - scale Variables. It also gives an example that Counts are interval scale measurements, such as counts of publications or citations, years of education. However, based on my understanding, 'counts' should be discrete variables.
Could anyone tell me why counts are continuous variables ? thanks !
 A: Discrete vs continuous: The real difference here is that the values that a discrete random variable can take are countable, while a continuous random variable takes values in some set of intervals -- its possible values are not countable.
For example, atmospheric pressure would generally be regarded as continuous.
The number of eggs laid by a chicken per day is discrete (you can count the possible values that it can take). Not all discrete random variables are integer, nor even equispaced.
Those two classes are not exhaustive - there are random variables that are neither (for example, mixtures of discrete and continuous).

The rest of the things you mention are from Stevens' typology of levels of measurement.
Stevens' levels are:
Nominal: The values are category labels (e.g. political affiliation, car color). They have no intrinsic order.
Ordinal: ordered categories (e.g. socioeconomic status, level of educational attainment). 
Interval: differences in two values are meaningful -- equal-sized differences mean the same thing (e.g. "5"-"3" is the same as "4"-"2". The classical example of this scale is temperatures (whether in Celcius or Farenheit). 
Ratio: Interval, with a meaningful zero, in such a way that equal ratios carry the same meaning -- "2" is twice as much as "1", "6" is three times as much as "2" and so on. The volume of water in a dam is ratio-scale.
Stevens' typology isn't the only possible categorization (there are other typologies), and you must beware people being overly prescriptive about this particular way of classifying variables; the level of measurement isn't necessarily inherent, but a matter of what questions you ask of the variable.
