Attribute, Discrete Variable, and Continuous Variable

Before explaining the answer, it is important to understand the terms attribute, discrete variable, and continuous variable.

- Attribute: An attribute is a characteristic that describes a person, place, thing, or concept. It can be qualitative or categorical in nature. Examples of attributes include gender, eye color, and nationality.
- Discrete Variable: A discrete variable is a type of quantitative variable that can only take on a finite number of possible values. The values are usually integers or whole numbers. Examples of discrete variables include the number of siblings a person has, the number of cars in a parking lot, and the number of pets in a household.
- Continuous Variable: A continuous variable is a type of quantitative variable that can take on an infinite number of possible values within a given range. The values can be any number, including decimals and fractions. Examples of continuous variables include height, weight, and temperature.

Answer Explanation

Based on the definitions above, the annual income of a person can be categorized as a discrete variable. This is because income can only take on a finite number of possible values, such as $50,000, $75,000, and $100,000. While income can technically take on an infinite number of possible values if you consider decimals and fractions, it is typically reported and measured in whole numbers or ranges.

Therefore, the correct answer is (b) a discrete variable.

Attribute, Discrete and Continuous Variables

An attribute is a characteristic or property of an object or a person. For example, the color of a car or the height of a person are attributes. Attributes are qualitative and do not have numerical values.

On the other hand, variables are quantitative and have numerical values. Variables can be further classified into two types: discrete and continuous.

- Discrete variables are those that can only take on specific values, usually integers. Examples of discrete variables include the number of children in a family or the number of pets in a household.
- Continuous variables, on the other hand, can take on any value within a certain range. Examples of continuous variables include height, weight, and temperature.

Annual Income as a Discrete Variable

Annual income is a quantitative variable, and it can be either discrete or continuous depending on the context. In most cases, annual income is a discrete variable because it can only take on specific values. For example, if we consider the US tax brackets for 2021, annual income can only take on the following values:

- $0 - $9,950
- $9,951 - $40,525
- $40,526 - $86,375
- $86,376 - $164,925
- $164,926 - $209,425
- $209,426 - $523,600
- $523,601 or more

Therefore, annual income is a discrete variable because it can only take on a finite number of values, and these values are usually integers or ranges of integers.

Conclusion

In conclusion, annual income is a quantitative variable, but it is usually considered a discrete variable because it can only take on specific values. Discrete variables are different from continuous variables, which can take on any value within a certain range.