What is the difference between a discrete random variable and a continuous random variable?

Hint: We first discuss the definitions of discrete random variable and a continuous random variable. We discuss their differences and also understand the concept with the use of different kinds of examples.

Complete answer:
The term variable means a character of an item or an individual that can be expressed in numerical terms. It is also a quantitative character which can be measured.
Variables can be classified in two parts – discrete and continuous.
A quantitative character that can take certain isolated values only in its range of variation is called a discrete variable.
We take an example to understand the concept better.
The number of heads when flipping three coins can be treated as a discrete variable. The choices are $0,1,2,3$.
A variable that can assume any value within its range of variation is called a continuous variable.
We take an example to understand the concept better.
The weight of individuals can be treated as a continuous variable.

Note: The thing to remember is that the recorded measurements may show some discreteness in case of continuous variable, but that’s merely artificial. This type of discreteness arises due to the limitations of the measuring instruments.