Pie chart

1Summary 重點摘要

Slices show % of whole.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: How a pie chart is builtA pie chart uses one whole circle for all the data, such as a class of 40 pupils, and each sector stands for one part, such as the pupils who love Maths. The relation between whole and parts is visible at a glance: the larger the share, the larger the sector, and all sectors together make exactly one circle. Why use a pie chart? Because it shows proportions of a whole better than a list of numbers ever could. A common misunderstanding is treating a sector as an independent amount; a sector is always only a part of the whole, so first confirm what the full circle stands for.
2. Step 2: Shares add to 100%The percentages of all parts must add up to 100%: for example Maths 25% + Chinese 40% + English 35% = 100%, fitting exactly one circle. Why must it be 100%? Because the whole circle is all the data, no part can lie outside it, and everything together is everything. If the parts do not sum to 100%, the data or the working has a mistake that must be found before drawing. A common error is rounding each part and drawing anyway with a total of 99% or 101%; the right move is to check the data and the arithmetic first, and only then pick up the compass.
3. Step 3: Percent to degreesThe whole circle is 360°, so a part of 25% takes a sector angle of 360 × 25% = 90°. Multiplying the percentage by 360° gives the angle, which is the key step in drawing a pie chart; measure the angle with a protractor and the sector follows. Why 360°? Because one full turn is exactly 360°, and multiplying by 360° shares the circle out in proportion. A common mistake is multiplying by 100, producing an impossible angle like 2500°; remember that no sector can exceed 360°, so any such answer is wrong before it is even drawn.
4. Step 4: Degrees per person40 people share the circle's 360°, so each person is worth 360 ÷ 40 = 9°; Chinese with 16 pupils takes 16 × 9° = 144°. Finding the degrees per person first and then multiplying by the count suits questions with whole-number counts, avoiding the conversion between fractions and percentages. Why does it work? Because every pupil occupies the same angle no matter the subject, so the count times the per-person angle gives the subject's total angle. A common error is computing the per-person angle wrongly, such as 90° instead of 9°; the drawn sector then overflows the circle, and a quick sum of angles reveals it.
5. Step 5: Degrees back to percentThe reverse also works: from an angle, find the share. A sector of 90° gives 90 ÷ 360 = 14 = 25%, a quarter of the circle. Dividing the angle by 360° and turning the result into a percentage lets drawing and reading flow both ways. Why is this allowed? Because angle and percentage are in proportion: the full 360° corresponds to 100% with a fixed scale, so a 180° sector is 180 ÷ 360 = 50%, exactly a semicircle. A common mistake is dividing by 100 instead of 360; keep in mind that the denominator is always the whole circle's 360°.
6. Step 6: Choosing the chartDifferent questions need different charts: to show what fraction each part takes of the whole, a pie chart fits best; to compare the amounts in each category, a bar chart is clearer; to see how a quantity changes over time, use a line graph. Charts are tools, so choose according to the message, for example a pie chart for the shares of a vote and a bar chart for comparing subject counts. A common mistake is picking a chart at random, such as a pie chart for temperatures over three months, which shows no trend at all; before choosing, be clear about the question the chart must answer.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Pie charts show each part's share of the whole
• All percentages add up to 100%
• Angle = percentage × 360°
• Read backwards: 90° ÷ 360° = 25%
• Shares → pie chart; comparisons → bar chart