A variable represents any characteristic, number, or quantity that can be measured or counted in a dataset. Numerical variables are a specific type that expresses measurable quantities as numbers. Understanding variables is fundamental in statistics for data analysis and drawing conclusions.
Understanding Numerical Variables
Numerical variables, also known as quantitative variables, represent measurable quantities. They indicate “how many” or “how much” of something there is. This type of data is inherently quantitative, meaning it deals with numerical values that can be ordered and subjected to mathematical operations like addition or subtraction. Common examples include a person’s age, height, weight, temperature, income, or the number of sales. These variables are essential for various statistical analyses, including calculating averages or identifying data patterns.
Discrete and Continuous Variables
Numerical variables are further categorized into two main types: discrete and continuous.
Discrete variables can only take on specific, distinct, and countable values, typically whole numbers. These values often result from counting items, such as the number of students in a classroom or the number of cars in a parking lot. A discrete variable cannot have fractional or decimal values between one count and the next; for example, you can have 20 or 21 cats, but not 20.5 cats.
Continuous variables, in contrast, can assume any value within a given range, including fractions and decimals. These variables are usually obtained through measurement rather than counting and can theoretically be subdivided infinitely. Examples include a person’s height, weight, time taken to complete a task, or temperature. While age is often treated as a discrete variable (e.g., age in years), it is fundamentally continuous because a person’s exact age includes months, days, hours, and even milliseconds. The distinction between discrete and continuous variables is important because they are described using different probability distributions in statistics.
Numerical vs. Categorical Variables
To understand numerical variables, it helps to differentiate them from categorical variables. Numerical data represents measurable quantities, while categorical variables describe qualities or characteristics. Categorical variables place observations into distinct groups or categories, often represented by non-numeric values. Examples include gender, eye color, or the type of car someone drives. Unlike numerical data, arithmetic operations typically cannot be meaningfully performed on categorical data. For instance, while you can count the number of males or females, you cannot perform addition or subtraction on “male” or “female” themselves. Sometimes, categorical variables might be assigned numeric labels, such as postal codes or identification numbers, but these numbers do not represent a measurable quantity and cannot be used in mathematical calculations.