Question

What are the differences between these discrete and continuous data? How might measuring them differ?

Answer 1

Suppose, X is the variable of interest. It will be classified as discrete or continuous by the definition of the variable.

If a variable can take only integer values then it will be classified as a discrete variable .Discrete data only assume certain values , like the no of arrivals in a given period. Here No of arrivals must be integer. Or the no of girls in the class.

if a variable can take integer as well as fractional values then it will be classified as a continuous variable.Continuous data can assume any values in the given range. E.g. Height of students, Weight of students

Let us consider a real life example in order to understand the difference between these two type of variables. Let X be the number of fish in a pond. It is impossible for X to be fractional number or a complex number, it has to be an integer number because as we know number of fish is a count which can be only an integer. Let us consider another example, in this case let X be the height of some students in a particular class. Here, it is not necessary for X to be an integer number, it can take any value within a valid range.

There are different type of probability distribution which can model these type of data, for example binomial distribution is a well known discrete distribution and normal distribution is a continuous distribution which is widely used to model these type of variables depending upon their definition.