Mathematics Year 7: From the study to the news: conclude, communicate, question
Mathematics, Year 7 (Portugal): Finish a study with a conclusion, a decision and a new question, tell its story to the right audience without misleading, and ask the same questions of a study reported in the news.
Conclude, decide, ask, then tell
A study ends in three steps. Conclusion: what the data show, with numbers. Decision: what to do because of it. New question: what is still unknown. Then you decide who to tell (classmates, families, the school board) and in what form (report, poster, infographic), and you tell the story: what you asked, what you found, what surprised you, what comes next. The communication must be rigorous, effective and not misleading.
A news item is always a summary
A news item about a study is always a summary, and every summary leaves things out. Whoever writes it chooses the headline, the graph, what goes in big letters. You need not distrust everything, but you should know what to ask: who did the study? How many people were asked, and how? What was left untold? Learning to ask these questions is statistical literacy, and it helps you read other people's news as well as tell your own study well.
“6 out of 10”: how many were asked?
A news item says: “6 out of 10 pupils prefer morning lessons”. Question 1: how many were asked? Case A: 10 pupils, 6 prefer: 6/10 = 60%. Case B: 1000 pupils, 600 prefer: 600/1000 = 60%. Same percentage. Question 2: how fragile is it? If one more pupil changed their mind, A would go from 60% to 7/10 = 70%, and B from 60% to 601/1000 = 60.1%. In A one pupil changes the result a lot; in B, hardly at all. So a percentage alone is not enough: you need to know how many were asked.
Right numbers, wrong picture
An infographic compares two values, 30 and 60, with a drawing of a book. Since 60 is double 30, the designer enlarges the book to double: double the height and double the width. But area is height × width: the first book has 1 × 1 = 1 and the second 2 × 2 = 4. The eye compares areas and sees a book 4 times bigger, when the value is only 2 times bigger. All the numbers are right and the picture still misleads. In a pictogram, repeat the same drawing the right number of times instead of enlarging it.
Questions for every news item
Use the questions of a study to read a news item: who did it, and with what source? How many people or cases does it cover? Compared with what, and over what period? Are the scale and the legend honest? What does the news not say? When you are the one telling, do the reverse: tell the story of the data, give the source and the number of cases, and end with a question for a future study. You meet this in news, social media and reports from associations.
Test what you learned
A class study will be shown to the school board. Which way of communicating it is rigorous, effective and not misleading?
- a) A poster with a bar graph starting at zero, a title, the source, one sentence of conclusion and a question for a future study
- b) The same graph with the axis cut at 40 so the differences show up more
- c) A big number with the mean alone, without saying how many pupils answered
- d) A table with all 200 answers in small print, so that nothing is left out
Correct answer: a) A poster with a bar graph starting at zero, a title, the source, one sentence of conclusion and a question for a future study — Right: honest scale, source and number of cases make it rigorous, one clear message makes it effective, and the new question tells the story forward.
Study A asked 10 pupils and 6 prefer morning lessons; study B asked 1000 and 600 prefer them. If one more pupil in each study also preferred mornings, what would the new percentages be?
- a) A: 61%, B: 61%
- b) A: 7%, B: 601%
- c) A: 70%, B: 70%
- d) A: 70%, B: 60.1%
Correct answer: d) A: 70%, B: 60.1% — 7/10 = 70% and 601/1000 = 60.1%. One pupil moves A by 10 points and B by only 0.1: the same 60% is fragile in A and solid in B.
An infographic shows 30 and 60 with the same drawing, but the drawing for 60 is twice as tall and twice as wide. About how many times bigger does its area look?
- a) 2 times, like the values
- b) 4 times, so the picture exaggerates a value that is only double
- c) 8 times, because 2 × 2 × 2 = 8
Correct answer: b) 4 times, so the picture exaggerates a value that is only double — Right: 2 × 2 = 4, against 1 × 1 = 1. The eye compares areas, so it sees 4 times where the value is 2 times.
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