Statistical Graphs

1Summary 重點摘要

Bar chart, line graph, pie chart — used to see data distribution and trends.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Bar charts: comparing categoriesA bar chart shows quantities as bar heights, ideal for comparing categories. Surveying the class's favourite subject: Chinese 8, English 12, Maths 10 — three bars of heights 8, 12 and 10 reveal at a glance that English leads. Bars must share one width with even gaps, and the vertical axis must start at 0; a truncated axis exaggerates small differences into apparent large ones, a classic distortion in newspaper charts, so stay alert whenever you read one.
2. Line graphs: showing trendsA line graph joins data points with segments to display change over time. Recording a week's temperatures — Mon 25°C, Tue 26°C, Wed 28°C, Thu 27°C, Fri 29°C — the connected line shows every rise and dip and even hints at the weekend ahead. The horizontal axis must be time or an ordered scale; plotting categories as a line makes the segments meaningless. Remember too that segments only guide the eye: they do not assert real values at the moments in between.
3. Pie charts: showing proportionsA pie chart shows each part's share of the whole as a sector. In a class of 40, the 10 who prefer Chinese fill a quarter of the circle (25%), the 16 preferring English take the largest sector (40%), and Maths takes 35%. All sectors must sum to the whole circle, that is 100%. Compute each sector's angle first: 25% corresponds to 360° × 0.25 = 90°. A pie shows proportions only, never totals — with two pies side by side, a bigger sector does not mean a bigger count, so read the totals too.
4. Setting up axes and scalesEvery statistical graph carries two axes: the horizontal axis holds categories or time — subjects, weekdays — while the vertical axis holds quantities such as headcounts or temperatures. Choose a sensible scale: with a maximum of 12 people, run the axis 0 to 15 with each grid square worth 3 or 5; squares too large flatten differences, too small push the drawing off the page. Always label the units — people, °C, items — or readers cannot judge what the numbers mean and the chart loses its force.
5. Four steps for reading a graphRead a graph in four steps: first the title, to know what it shows; second the axes, to confirm what each represents and its units; third the data, spotting highs, lows, rises and falls; fourth a conclusion in one sentence, such as 'temperatures rose about 4°C this week' for a line moving from 25°C to 29°C. While reading, also check whether the scale starts at 0, guarding yourself against exaggerated visual effects that distort the story the data actually tells.
6. Choosing the right chartChoose by purpose: compare categories with a bar chart, show change over time with a line graph, show parts of a whole with a pie chart. Comparing student numbers per subject calls for bars; a year of temperatures calls for a line; the class's subject preferences call for a pie. The wrong choice buries the message — headcounts drawn as a pie force readers to compute numbers in their heads, far less direct than bars. In answers, name the chart type first and then justify it; both parts are needed for full credit.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Bar chart: compare categories
• Line graph: see trend
• Pie chart: see proportion
• y-axis starts at 0
• Graph needs title and labels