Construct circle graphs

Constructing a circle graph represents categorical data as sectors of one circle, with each sector’s central angle proportional to its category frequency: $(\text{category count} \div \text{total}) \times 360^\circ$ , or the equivalent percentage of $360^\circ$ . The learner calculates or estimates angles for common fractions and percentages, labels sectors, and verifies that the angles total $360^\circ$ ; the scope excludes three-dimensional charts, statistical inference, and more advanced data transformations.

Detailed Explanation: Construct circle graphs

A circle graph shows each category as a sector, or “slice,” of one circle. The size of each slice depends on the category’s share of the total.

Use this formula:

\text{central angle}=\frac{\text{category count}}{\text{total count}}\times 360^\circ

Example: A class surveys 20 students about their favorite fruit.

Fruit	Number of students
Apples	8
Bananas	6
Oranges	4
Grapes	2

1. Find the total

The total is already given as 20. You can check it:

8+6+4+2=20

2. Find the angle for each category

For apples:

\frac{8}{20}\times 360^\circ=144^\circ

For bananas:

\frac{6}{20}\times 360^\circ=108^\circ

For oranges:

\frac{4}{20}\times 360^\circ=72^\circ

For grapes:

\frac{2}{20}\times 360^\circ=36^\circ

Your angle table is:

Fruit	Angle
Apples	$(144^\circ)$
Bananas	$(108^\circ)$
Oranges	$(72^\circ)$
Grapes	$(36^\circ)$

3. Draw and label the circle

Use a compass or a circular template to draw one circle.
Draw a radius from the center to the edge.
Use a protractor to measure $(144^\circ)$ from that radius. Label the sector Apples.
From the new radius, measure $(108^\circ)$ . Label the next sector Bananas.
Measure $(72^\circ)$ for Oranges.
The remaining sector should be $(36^\circ)$ . Label it Grapes.
Add a key or label each sector clearly.

4. Check your work

All sectors must make one full circle:

144^\circ+108^\circ+72^\circ+36^\circ=360^\circ

Since the angles total $(360^\circ)$ , the circle graph is complete.

Learn by doing: Construct circle graphs

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Graphing - Create Circle Graph (Percent) from Data (Pictures)

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