Lesson 27: Pie Charts and Bar Charts

§Text Passage

1Summary 重點摘要

Pie chart shows proportion (each category % of total), bar chart shows comparison (which is more/less). Learn to read charts, calculate angles and draw.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Pie Chart: Calculate AngleIn a pie chart, each category's angle = (category count ÷ total) × 360°. For example, in a class of 40 with 10 pupils loving Maths most, the Maths sector = (10 ÷ 40) × 360° = 0.25 × 360° = 90°, exactly a quarter circle. Why find the share before multiplying by 360°? Because the angle is allocated in proportion to the category's share of the whole: the share is some fraction, and the angle is that fraction of 360°. A common error is using the count as the angle directly, treating 10 pupils as 10°, which leaves all sectors far short of a full circle; the order is always divide first, multiply second, never reversed.
2. Block 2: Pie Chart: PercentageEach category's percentage of the whole = (category count ÷ total) × 100%. For example 10 ÷ 40 = 0.25 = 25%, one quarter. Percentage and angle correspond one to one in a pie chart: 25% matches 90°, 50% matches 180°, and 12.5% matches 45°, so the two forms check each other. Why one to one? Because 100% corresponds to 360° with a fixed scale, and multiplying a percentage by 3.6 gives the angle. A common error is mixing the two forms, answering 25% when the angle was asked; read which one the question wants, convert with a multiplication or division by 3.6, and confirm the unit before writing the answer.
3. Block 3: Bar Chart: ReadTo read a bar chart, look at the vertical axis scale first, then at where each bar's top reaches. For example, a Maths bar reaching the mark 10 means 10 people. Longer bars mean larger numbers, but the value of each grid line matters: 2 per line and 5 per line give completely different readings at the same height. Why the scale first? Because the grid value is decided by whoever drew the chart and is not fixed at 1; skipping the scale and counting grid lines alone goes wrong. A common error is ignoring the grid value and reading 4 lines as 4 people when it is really 20; the first step of reading is always confirming the grid value.
4. Block 4: Pie vs BarThe two charts have different strengths: the pie chart excels at showing proportions, answering questions like 'what fraction of the class chose Maths?'; the bar chart excels at comparisons, answering 'is Maths more than Chinese?'. Why the division of labour? Because the pie highlights part against whole while the bar highlights ranking among categories, and only the right chart carries the message clearly — shares of subject choices go to the pie, comparisons of subject counts go to the bar. A common error is a wrong chart choice, such as comparing five classes' book counts with a pie chart, where the ranking becomes hard to see; decide what to express before choosing.
5. Block 5: Draw Pie Chart StepsDrawing a pie chart takes four steps: first work out each category's percentage; second multiply each percentage by 360° to get its angle; third draw the sectors one by one on the circle with a protractor; fourth colour them differently and add a title. Why must the order hold? Because each step uses the previous step's results: without the percentages the angles cannot be found, and without the angles no sector can be drawn. All sector angles must add up to exactly 360°, which serves as the final check. A common error is missing a category, or misplacing the protractor's centre so the angles come out wrong; after drawing, add up every angle and confirm 360°.
6. Block 6: Reading PitfallsReading charts has two common traps: a pie chart without printed numbers must be worked out from the proportions rather than guessed, and a bar chart whose vertical axis does not start at 0 exaggerates the gaps between bars, making differences look far larger than they are. Why does the starting point matter so much? Because comparing bars by eye relies on their full height, and a raised starting point inflates the gap, deceiving the eye. Check the scale and the units before drawing any conclusion, and never be misled by appearance alone. A common error is taking two very unequal bars as a huge data gap; examine the axis start first, then judge the real size of the difference.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Pie chart: see proportion
• Bar chart: see comparison
• Pie chart total 360°
• Angle = (category ÷ total) × 360°
• Draw pie chart with protractor