**Discrete Variable:**

A discrete variable is a type of variable that can only take on specific values within a specific range. These values are typically whole numbers or integers. Discrete variables are often used to represent counts or categories. Here are some key characteristics of discrete variables:

1. **Distinct Values**: Discrete variables have distinct and separate values. For example, the number of children in a family can only be whole numbers such as 1, 2, 3, and so on. You cannot have 1.5 children.

2. **Countable**: Discrete variables can be counted or enumerated. They represent individual units or categories. For instance, the number of cars parked in a parking lot can be counted.

3. **Finite or Infinite**: Discrete variables can have either a finite or an infinite number of possible values. For example, the number of siblings a person has is a discrete variable with a finite number of values, while the number of people in a city is a discrete variable with an infinite number of values.

4. **Non-Continuous**: Discrete variables cannot take on any value within a given range. There are gaps between the possible values. For instance, if a variable represents the number of pets owned by people, it can only have values like 0, 1, 2, 3, and so on. It cannot have values like 1.5 or 2.75.

**Continuous Variable:**

A continuous variable is a type of variable that can take on any value within a specific range. Continuous variables are typically measured on a continuous scale and can include decimal numbers. Here are some key characteristics of continuous variables:

1. **Infinite Possible Values**: Continuous variables can have an infinite number of possible values within a given range. For example, the height of individuals can be measured in inches or centimeters and can take on any value within a range.

2. **Measurable**: Continuous variables can be measured with great precision using various instruments or tools. For instance, temperature can be measured using a thermometer, allowing for precise measurement.

3. **Continuous Range**: Continuous variables have a continuous range of values. There are no gaps or jumps between the possible values. For example, a variable representing the weight of individuals can take on values like 50.2 kg, 50.3 kg, 50.4 kg, and so on, allowing for any decimal value within a range.

4. **Infinite Precision**: Continuous variables can be measured with infinite precision, although practical limitations of measurement tools may result in rounding or limited precision in practice.

**Summary:**

In summary, the main difference between discrete and continuous variables lies in the nature of their possible values. Discrete variables can only take on specific, distinct values, often representing counts or categories. On the other hand, continuous variables can take on any value within a specific range and can be measured with great precision. Understanding the distinction between these types of variables is crucial in various fields, including statistics, mathematics, and data analysis.

Discrete variable it assume only by countable number (0,1,2,3,4,6.... etc) whole number example:number of error in book and number of atoms in element etc.

continuous variable it assume any value of given interval(0.1,1,1.5,1.7,2,2.5....etc) decimal and whole number example:weight,hight,age marks etc.