L3 · Circle Graphs: Building from Percents

Learning goal

“I can represent categorical data in a circle graph: turn counts into percents of the whole, turn each percent into a central angle (percent x 360°), draw and label every sector - and check that the percents sum to 100% and the angles sum to 360°. Each sector is PROPORTIONAL: its share of the circle equals its share of the data.”

Categorical data — data sorted into categories (ways to travel, favourite fruits). This is the kind of data a circle graph shows.

Sector — one slice of the circle, standing for one category.

Central angle — the angle at the centre of the circle that opens up a sector; it decides how big the slice is.

Proportional — each sector's angle is the same fraction of 360° as its category is of the whole data: a category with twice the percent gets twice the angle.

Worked example

A survey of 200 students asked how they get to school. Results: Walk 35%, Bus 30%, Car 25%, Bike 10%. Step 1: Check the shares: 35 + 30 + 25 + 10 = 100%. Good - the parts make the whole. Step 2: The whole circle is 360°, so each category gets its percent OF 360°: Walk: 35% x 360° = 126°. Bus: 30% x 360° = 108°. Car: 25% x 360° = 90°. Bike: 10% x 360° = 36°. Step 3: Check the angles: 126 + 108 + 90 + 36 = 360°. Good. Step 4: Draw each sector with a protractor and label it with the category name AND its percent. A sector without a label is just a slice. Say it plainly: the sectors are PROPORTIONAL - Walk has 3.5 times Bike's percent (35% vs 10%), and it gets exactly 3.5 times Bike's angle (126° vs 36°). That is what makes the graph honest.

Check yourself — explain it

A category's percent doubles. What happens to its central angle?

Paired problem — example still visible

Favourite colour in a class: Red 20%, Blue 45%, Green 25%, Yellow 10%. Find the four central angles. -> Red 72°, Blue 162°, Green 90°, Yellow 36° (sum 360°)

Faded completion — last step is yours

"Magazines are 15% of a library's loans. The sector angle: 15% x 360° = ___." -> 54°

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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