ACT® · Math: Statistics and Probability — Describing Data
Translating One Data Representation into Another
The same data can appear as a bar graph or a circle graph; converting between them means turning each category's fraction of the total into either a bar height or a slice angle out of 360 degrees.
A bar graph and a circle graph can show identical numbers and still feel like different stories, because a bar graph lets you compare raw counts side by side, while a circle graph only shows each category's share of the whole. Redrawing one as the other does not change any data. It just changes which comparison jumps out at you first: absolute size versus proportion.
The conversion runs on one idea: a full circle is 360 degrees, and that 360 represents everyone in the survey. If a category has k people out of n total, its slice gets the same fraction of 360 that k is of n. So the central angle is (k/n) times 360. This means you never need the actual bar heights, just each category's count and the total count.
This connects directly to the rest of describing-data questions, since both bar graphs and circle graphs are just different pictures of the same frequency table you might also see turned into a two-way table or used to find a mean. The catch that trips people up is totals: a circle graph always has to account for 100% of the group, so if the bar graph's categories do not add up to the full survey, the circle graph needs an extra slice for whoever is missing, or the picture is wrong.
Key terms
- Central angle
- The angle at the center of a circle graph that a single slice takes up, out of 360 degrees total.
- Frequency
- The count of how many people or items fall into one category.
- Proportion
- A category's count divided by the total count, showing its share of the whole group.
- Circle graph
- A chart where the full circle represents the whole group and each slice's angle shows a category's share of it.
Watch it explained
- How it worksHow does each category's share of the total become a slice angle in a circle graph?
- Worked exampleFind the central angle of the slice for 15 students out of 60 when a bar graph is redrawn as a circle graph.
- Going furtherWhat happens to a circle graph when the bar graph's categories do not add up to the whole group?
Check yourself
End of topic.