Question

How Are Age and Income Related? An economist collects data from many people to determine how age and income are related. How the data is collected determines whether the variables are quantitative or categorical. Describe how the information might be recorded if we regard both variables as quantitative. Then describe a different way to record information about these two variables that would make the variables categorical.

Short answer

Age and income can both be recorded as quantitative and categorical variables. As quantitative variables, age and income could be recorded in their actual numeric form, e.g., 30 years old, $50,000 income. Treating them as categorical variables would involve grouping them into categories. For instance, age could be categorized as 'Young', 'Middle-aged', and 'Senior' and income could be grouped into 'Low', 'Medium', and 'High'.

Step-by-step solution

Understand Quantitative and Categorical Variables

Quantitative variables are numeric and measurable. They usually represent a counted or measured quantity like age or income. Categorical variables, on the other hand, are qualitative and represent characteristics or categories. They're often based on qualitative attributes like gender or city.

Record Data with Quantitative Variables

If age and income are regarded as quantitative variables, the data could be recorded in a direct numeric form. For instance, age could be recorded in years, and income could be recorded in dollars. An example of such a record might be: 25, $40,000 - representing a 25-year-old person earning $40,000 per year.

Record Data with Categorical Variables

To treat age and income as categorical variables, they'd need to be grouped into categories. For Age, categories like 'Young Adult (21-35)', 'Middle-aged (36-60)', 'Senior Citizen (60+)' could be used. Similarly, for income, categories could be 'Low income (<$30,000)', 'Middle income ($30,000-$60,000)', 'High income (>$60,000)' could be used. Thus, a record might look like this - 'Young Adult (21-35)', 'Middle income'.