The parallel boxplots shown display thedistribution of battery life (in hours) for twobrands of batteries (brand A and brand B). The variables battery life and brand are:

Question

BlackTom AI · Accepted Answer

To determine the nature of the variables, we examine what each variable represents in the plot.
Option a: 'a categorical and a numerical variable respectively' would imply the first variable is categorical and the second is numerical. In the boxplot, the first variable shown is the brand (A vs B), which is a category, but the second variable is battery life in hours, which is numerical. Since the order in the statement would be brand first then battery life, this option would be mixing the roles incorrectly if interpreted as presented in the question context.
Option b: 'a numerical and a categorical variable respectively' corresponds to battery life as numerical (continuous measurements in hours) and brand as categorical (A or B), which matches what the boxplots display: the distribution of a numerical measure (hours) across categories (brands).
Option c: 'both categorical variables' would imply both axes show categories, which is not the case here since boxplots summarize numerical data and show spread/center of battery life per category.
Option d: 'both numerical variables' would indicate two numerical axes or two numerical distributions without categorical grouping; the presence of two separate boxplots by brand indicates a grouping by a categorical variable, not two numerical variables.
In summary, the plots depict battery life as a numerical variable measured in hours, compared across two brands which form a categorical grouping. Therefore, the correct characterization is that battery life is numerical and brand is categorical.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025 3.6 Comparing Univariate Data Quiz (Formative)

The parallel boxplots shown display thedistribution of battery life (in hours) for twobrands of batteries (brand A and brand B). The variables battery life and brand are:

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The parallel boxplots shown display thedistribution of battery life (in hours) for twobrands of batteries (brand A and brand B). The variables battery life and brand are:

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