How a decorated graph can mislead an honest reader

What to assume they know

• What makes a data picture clear and worth looking at — why bar direction and clarity matter
• Reading a bar graph: what length is standing for — that a bar graph works by equal widths and a scale marked in equal steps
• Doubling a four-digit number, and comparing the result with another
• Reading a value off a marked scale
• Comparing two four-digit numbers

What they should be able to do

• Define an infographic as a data display with substantial artistic imagery added, and say what it is for
• Identify a second visual signal — width, area, shape — that a decorated graph introduces without declaring it
• Explain why the bars of a bar graph are given a common width
• Test a visual impression against the numbers by computing, using the book's own doubling check
• Judge whether a given infographic preserves the quantity it claims to show
• State that the risk runs both ways: you can be misled by someone else's picture and can mislead others with your own
• List what to check before trusting a decorated data picture

Where it usually goes wrong

• "A prettier graph is a better graph." The book's own sequence goes the other way: each beautification step on pp.104–105 makes the picture more attractive and less trustworthy. Attractiveness and fidelity are separate axes.
• "The triangles are fine because their tops are at the right heights." They are. The problem is what else changed while nobody was watching. A picture makes every claim its geometry makes, not only the intended one.
• "Infographics are a trick, so avoid them." The book does not say that. It says they are made to communicate quickly and pleasingly, and that they need checking. The verdict it invites is care, not refusal.
• "Only dishonest people make misleading graphs." The book's own word for what happens here is the adverb accidentally (p.104). Nobody in the example is trying to deceive; the drawing acquired an extra meaning while being made prettier.
• "Everest is about twice Elbrus — the picture shows it." Double 5642 and compare with 8848. Everest is well short of twice Elbrus, and the picture is the only thing that said otherwise.
• "If the label is printed on the picture, the picture is accurate." The mountain-range infographic carries correct-looking labels and still distorts the relative heights — and one of its labels disagrees by 3 m with the table it came from.
• "This is about art, so there is no right answer." There is: a picture either preserves the quantities or it does not, and that is decidable by arithmetic.

Questions to check understanding

Class 6 has no board paper; these are the shapes the book uses and that school and competency-based assessments repeat:

• Given a decorated data picture, state what it shows correctly and what it implies that the data does not support
• Explain why the bars of a bar graph are drawn with the same width
• Test a stated visual impression ("A looks twice B") by computing, and report whether it holds
• Redraw a misleading infographic as a plain bar graph and say what changed
• Given a table and a picture, find where they disagree
• Explain in one sentence what an infographic is and what it is for
• Say what you would check before believing a graph you saw in a newspaper

Examples worth working on the board

• The seven heights, once more (p.101, carried into pp.104–105). Everest 8848 m, Aconcagua 6962 m, Denali 6194 m, Kilimanjaro 5895 m, Elbrus 5642 m, Vinson Massif 4892 m, Koscuiszko 2228 m. Every claim in this topic is tested against these seven numbers.
• The triangle infographic (p.104). The seven summits as coloured triangles above a scale marked 1000 m to 8000 m, each labelled with its mountain, its height and its continent. The apex of each triangle is at the right height. The base of each triangle is not constant — the taller ones are visibly broader. That mismatch is the entire lesson.
• The book's own objection (p.104). It points out that in the plain graph each rectangle was given the height its number required and a width identical to every other rectangle's, so that height alone was under comparison. It then asks the reader directly whether a taller mountain is invariably a broader one, and concludes that the decorated picture is asserting an extra thing which may well be false.
• The mountain-range infographic (p.105). A single painted range with the seven summits picked out on it, each labelled with name, continent and height, under a caption naming them as the highest peaks, continent by continent. The book asks whether it is better than the plain column graph, and whether it is accurate.
• The doubling test (pp.104–105). The book observes that in that picture Everest appears about twice as tall as Elbrus, and then asks a single arithmetic question: what is 5642 × 2? Do not give it the product — the whole beat is the student computing it and comparing it with 8848.
• The internal disagreement (pp.101, 104, 105). Kilimanjaro is printed at 5895 m in the table on p.101 and on the triangle infographic on p.104, but at 5892 m on the mountain-range infographic on p.105. Both pages were checked. Use it, carefully, as evidence that decorated pictures are where labelling slips creep in.
• The two-sided warning (p.105). The section closes by asking for care in two directions at once — making such a picture, and reading one — so that an audience is not led astray and the maker is not fooled either.

Figures to have open

• The triangle infographic (p.104) with its scale strip. Drawn artwork; must come from a printed page. It cannot be reconstructed from the extracted text — the varying base widths, which are the entire point, exist only in the drawing.
• The mountain-range infographic (p.105) with its seven labelled peaks and its caption. Drawn artwork. Reproduce neither directly; redraw a range with the same seven labelled summits so the distortion can be shown and then corrected.
• The plain column graph (p.102) as the honest comparison. Drawn artwork. The topic needs all three pictures side by side at least once.
• A width-measuring overlay for the triangles: seven vertical bases with their widths marked. Standard schematic; this is an addition made here and is the clearest way to expose the second signal.
• A two-bar comparison of 8848 against 2 × 5642, drawn to a common scale. Standard schematic.

Where this sits in the book

• NCERT Class 6 Mathematics (Ganita Prakash), Chapter 4 "Data Handling and Presentation". The material for this topic sits under the unnumbered heading "Infographics", pp.103–105, which follows the "Figure it Out" of §4.5. Because that heading carries no number, cite it by name and page rather than by section number.
• The definition of an infographic, p.103; the triangle infographic and the book's objection to it, p.104; the mountain-range infographic, the doubling question and the closing warning, p.105.
• §4.5 "Artistic and Aesthetic Considerations", pp.101–103 — the seven-summit table and the honest graphs this topic tests the decorated ones against.
• §4.3 "Bar Graphs", p.86 — where uniform width is first required.
• Chapter Summary, p.106 — the penultimate bullet, that making a data picture fancy can sometimes mislead.
• Back pointer: What makes a data picture clear and worth looking at. This is the last topic of the chapter.