Lesson 28: Statistics Applications

§Text Passage

1Summary 重點摘要

Statistics applications: read charts, compare data, draw conclusions. Learn to find answers, compare and ask questions from graphs.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: First: Read TitleWith any statistical chart in hand, the first job is reading the title and working out what the chart is about. For example, a title reading 'P6 Pupils' Favourite Subjects' tells you the chart surveys subject preferences, with headcounts as the data. Why the title first? Because the same numbers mean entirely different things under different themes, and reading figures before the theme easily heads the wrong way, mistaking people for marks. A common error is skipping the title and studying the bars, then answering off the point; reading always starts at the title and moves to the units next, with the order never shuffled.
2. Block 2: Read AxesSecond, read the two axes: the vertical axis usually carries the amounts and the horizontal axis the categories. For example, the vertical axis shows pupil numbers from 0 to 20 with each grid line worth 2, and the horizontal axis lists Maths, Chinese, English and General Studies. Why must each grid's value be clear? Because the scale is not fixed at 1 per line, and every reading must be converted by the grid value: a bar reaching the 4th line means 4 × 2 = 8 pupils. A common error is ignoring the grid value and reading every line as 1, getting every figure wrong; confirm the starting point and the grid value before reading anything.
3. Block 3: Find NumbersThird, read the figures off bar by bar: the Maths bar reaches 8, meaning 8 pupils like Maths most; Chinese reaches 12, English 6, and General Studies 4. Tick each bar as you read it, making sure every bar is covered and no category is missed. Why read bar by bar? Because statistics questions usually need the whole dataset, and missing one bar spoils the totals and the comparisons that follow. A common error is reading only the tallest and the shortest bars and dropping the middle ones, with the shortage surfacing only at the total; keep the habit of recording every figure before any calculating begins.
4. Block 4: CompareOnce the numbers are read, compare them: Chinese is the largest with 12 pupils, General Studies the smallest with 4; the gap is 12 - 4 = 8 pupils, and Chinese is three times General Studies. Three good questions guide the comparison: which is the largest, which the smallest, and by how much do they differ? Why watch both the difference and the multiple? Because word problems ask both, and the two wordings call on subtraction and division respectively, so thinking them through beforehand prevents panic later. A common error is describing a gap of 8 as twice as many; 8 more is actually two extra portions, meaning three times the original, and the wording must be exact.
5. Block 5: Draw ConclusionThe last step of statistics is drawing a conclusion from the data: this chart shows P6 pupils like Chinese most and General Studies least. A conclusion can carry a suggestion too, such as adding more activities to make General Studies more attractive. Why must a conclusion rest on data? Because statistics speaks with numbers, and a conclusion without them is only a feeling; saying simply that nobody likes the subject, without the figure of 4 pupils, is far less convincing. A common error is a conclusion detached from the data, or an exaggerated one, turning 4 pupils into nobody; conclusions must stay faithful to the numbers, neither inflated nor shrunk.
6. Block 6: Watch for MisleadingSome charts mislead their readers: for example, if the vertical axis starts at 3 instead of 0, the gap between two bars looks far bigger than it really is. Why the distortion? Because the bars' visual height has been cut off at the base, exaggerating the gap, and a reader comparing by eye is deceived. When reading a chart, check where the scale starts, how big each grid step is, and what the units are; never trust the first visual impression of the bars alone. A common error is being persuaded by an exaggerated chart, believing two subjects differ hugely when the real gap is 2 pupils; checking the axis start before judging is the basic defence.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Reading: title → axes → numbers → compare → conclusion
• Statistics helps make decisions
• Most popular = most people chose
• Watch for misleading charts
• Add numbers = total people