Which graph effectively shows the frequency of occurrence in categories of qualitative data?

A bar graph is the most effective way to show the frequency of occurrence in categories of qualitative data because it visually represents each category with rectangular bars, where the length or height of each bar corresponds to the frequency or count of observations in that category. This allows for easy comparison among different categories, making it clear which categories have higher or lower occurrences.

In contrast, a line chart is typically used to display quantitative data over a period of time, focusing on the trends rather than categorical comparisons. A Pareto chart, while also valuable for qualitative data, specifically emphasizes the largest problems or categories in terms of frequency, usually in descending order, but is fundamentally a type of bar graph tailored for identifying priorities. Lastly, a box plot is primarily used for displaying the distribution of quantitative data and highlighting medians and quartiles, which does not effectively represent categorical frequencies. Thus, the bar graph best fulfills the requirement of showing frequency in categories of qualitative data.