The variables number of cars owned and car size (small, medium, large) are:

Question

BlackTom AI · Accepted Answer

Here's how to analyze the question about variable types step by step.
Option a: 'both categorical variables' — This would imply number of cars owned is treated as a category (e.g., 1 car, 2 cars, 3 cars) and car size is a category (small, medium, large). However, the number of cars owned is inherently a count and is best described as numerical data, not just a label. So labeling both as categorical would ignore the numeric meaning of counts.
Option b: 'both numerical variables' — This would treat number of cars owned as numerical (a count) and car size as numerical (which it is not; 'small', 'medium', 'large' represent qualitative categories, not a numeric scale). Therefore, this option misclassifies car size as a number, which is inaccurate for typical data coding in statistics.
Option c: 'a categorical and a numerical variable respectively' — This suggests the first variable is categorical and the second is numerical. But number of cars owned is a count (numerical), while car size is categorical. If we map the order as given (number of cars owned first, then car size), this option mislabels the first variable and would not align with how the data are typically coded.
Option d: 'a numerical and a categorical variable respectively' — This matches the intuitive and standard classification: number of cars owned is a numerical (count) variable, while car size (small, medium, large) is a categorical (ordinal/non-numeric) variable. The word 'respectively' ties the first and second items in the same order as the question, which aligns correctly with the definitions of the two variables.
In summary, when evaluating variable types, the number of cars owned is a countable quantity and thus numerical, whereas car size is a qualitative descriptor that falls into the categorical category. Recognizing these distinctions helps prevent mislabeling a qualitative measure as numerical or vice versa.

The variables number of cars owned and car size (small, medium, large) are:

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