L4 · Reading Circle Graphs; Comparing Representations of the Same Data

Learning goal

“I can analyze a circle graph to solve problems: turn a sector's angle or percent back into a count when I know the whole, find a missing category, and compare two representations of the same data - knowing that a percent only becomes a count through its own whole, so the same percent in two graphs can stand for different counts.”

Representation — a way of showing data: a table, a bar graph, a circle graph, a histogram. Each representation shows some things well and hides others.

Whole — the total the full circle stands for (for example, all 600 students in a school). You must know the whole to turn a percent into a count.

Estimate — to read an approximate value from a graph when exact numbers are not labelled, using benchmarks like 25% (a quarter of the circle, 90°).

Worked example

A circle graph shows how the 600 students of a school get to school. Sectors: Walk 30% (108°), Bus 45% (162°), Car 15% (54°), Bike 10% (36°). Step 1: A percent becomes a count only through the WHOLE: count = percent x whole. Step 2: Walk: 30% of 600 = 180. Bus: 45% of 600 = 270. Car: 15% of 600 = 90. Bike: 10% of 600 = 60. Step 3: Check: 180 + 270 + 90 + 60 = 600 - the counts rebuild the whole. Step 4: Working from an ANGLE instead: percent = angle / 360°. A sector of 162° is 162/360 = 45% - then proceed as above. Say it plainly: a circle graph by itself speaks in SHARES. Counts live one step away, through the whole - and if you don't know the whole, counts cannot be recovered at all.

Check yourself — explain it

Why can't you find HOW MANY students walk from the circle graph alone, without being told the school has 600 students?

Paired problem — example still visible

A circle graph of 300 students: Bus 40%, Walk 35%, Car 25%. Find how many students each sector stands for. -> Bus 120, Walk 105, Car 75 (sum 300)

Faded completion — last step is yours

"A sector has a central angle of 108°. Its percent is 108 / 360 = ___%. Out of 500 students, that sector stands for ___ students." -> 30%; 150

Ready to practise?

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

Start practice →Take the unit quiz