What is a variable? Distinguish between a discrete and a continuous variable.
Variables are broadly classified into two types based on specific criteria: continuous and discrete. A continuous variable can take any numerical value, including integral values, fractional values, and values that are not exact fractions. Its values can be broken down into infinite gradations. Examples include height, weight, time, and distance.
A discrete variable, on the other hand, can take only certain values. Its value changes only by finite “jumps” from one value to another, and it does not take any intermediate value between them. For example, the “number of students” can only be whole numbers; it cannot take fractional values like 0.5. Even if a discrete variable takes fractional values like 1/8 or 1/16, it cannot take values between two adjacent fractions.
Explanation
The textbook context defines variables by their classification into continuous and discrete types. It explains that a continuous variable takes any value (integral or fractional) and can be broken into infinite gradations (e.g., height, weight). In contrast, a discrete variable takes specific values and changes by finite 'jumps' without intermediate values (e.g., number of students). The answer strictly adheres to these definitions and examples provided in the text chunks.