Explain the difference between categorical, ordinal, interval, ...

[rl]

Explain the difference between categorical, ordinal, interval, and ratio data. Give an example for each.
 
  What will be an ideal response?

Question 2

What is the probability that the system is not empty?
 
  A) 0.60
  B) 0.40
  C) 0.83
  D) 0.17

[frejo]

Answer to Question 1

Categorical data are sorted into categories according to specified characteristics. The categories bear no quantitative relationship to one another, for example, gender. Ordinal data are ordered in rank according to some relationship to one another; they are categorical but also have a natural order. An example would be the separation of students based on class (freshman, sophomore, junior, senior). Interval data are ordered, have a specified measure of distance between observations but have no natural zero. Interval data allow meaningful comparison of ranges, averages and other statistics where ordinal data do not. The difference between the two values are meaningful, however, the ratio is not. SAT scores are an example of interval data. Ratio data are hierarchical in that each level includes all of the information content of the one preceding it. Ratio data have a natural zero where interval data do not. Both difference and ratio of two values are meaningful. Salaries in dollars are an example of ratio data.

Answer to Question 2

C