What does a bar graph primarily represent?

A bar graph is designed predominantly to represent categorical data. In a bar graph, various categories or groups are displayed on one axis, while the length or height of the bars represents the quantity associated with each category. This visual format allows for easy comparisons between different groups or categories, highlighting the disparities in their respective values.

For example, if you have a bar graph showing the favorite fruits of a group of people, each bar would represent a type of fruit (like apples, bananas, oranges), and the height of each bar would indicate how many people preferred each fruit. This makes it straightforward to see which fruit is the most or least popular.

The other options focus on different types of data representation. Proportional relationships and slices of a whole typically relate to pie charts, which emphasize parts of a whole rather than distinct categories. Trends over time are usually represented using line graphs that illustrate changes in data points across a time continuum. Hence, while those other forms of representation serve their purposes well, they do not capture the essence of what bar graphs depict, which is the comparison of quantities across different categorical data points.