Telling tall tales: how a truthful graph still misleads

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

Why one number is never enough to describe a data set — a group's average says nothing about any one member
Clustered bar graphs: comparing across categories and across time — reading a clustered graph, and stating its scale
Dot plots: seeing spread and clustering at a glance — comparing two dot plots drawn on one scale
Reading a four-column-pair table and locating a cell by row and column
Comparing decimals to one place

What they should be able to do

Judge whether a stated claim is supported by a given table or graph, and give the reason either way
Explain why data from one or two schools cannot settle a question about all children
Distinguish a claim about averages from a claim about every individual
Read a graph whose vertical line does not begin at zero, and say what the choice does to how the differences look
Estimate a value from a bar that carries no printed number, and label the answer as an estimate
Spot a claim that a graph could not settle because the graph is not about that quantity at all
Extend a trend cautiously, and say what makes an extrapolation risky

Where it usually goes wrong

"If the graph is accurate, the conclusion is safe." Every figure in this section is accurate. All the errors on offer are errors of scope, and none of them would be caught by checking the numbers.
"A pattern in two schools is a pattern in general." The chapter says the opposite outright, and its own twelve means are the counter-example: the boys-versus-girls comparison does not even agree with itself from one grade to the next.
"'Girls of this age are taller on average' means every girl is taller." The fourth statement on p.127 is written to catch exactly this, and the same trap was already sprung once in §5.2 with the Class 5 classroom. Two exposures, one error — name it as the same error both times.
"A vertical line that does not start at zero is dishonest." Not the chapter's position and not a fair one. It is a choice with a stated purpose. The discipline is to notice it, say what it is doing, and refuse to eyeball a ratio off a truncated picture.
"A bar with no number on it cannot be used." It can be estimated, to the precision the markings allow, and the answer stated as an estimate. Three bars on the skyscraper chart are unlabelled on purpose.
"The longest bar means the biggest / tallest / best." On the skyscraper chart the longest bar means the most buildings over 150 m. It says nothing about which is tallest. Always read the quantity, not the ranking.
"A trend can be extended as far as you like." The table stops at 19 because the survey stopped at 19. The 2029 estimate the chapter asks for is a reasonable exercise; a 2129 estimate would not be, and the difference is worth a sentence.
"Whichever data set is bigger is right." The national table is far bigger than the two schools' worth of dots, and it still cannot say anything about a named child. Size fixes some problems of scope and not others.

Questions to check understanding

"Say which of these claims the table justifies, and which it does not" — with a reason attached to each, which is where the marks sit
Find a counter-example in a table that defeats a stated generalisation
Estimate a value from an unlabelled bar and state the precision of the estimate
Explain what changes when a graph's value line starts above zero
Given a survey of one school, say what it can and cannot be used to conclude
Rewrite an over-reaching claim so that the data does support it
Extend a trend by one step and say what would make the extension unsafe
Given a chart, name the quantity it measures and identify a question it cannot answer

Examples worth working on the board

The twelve school dot plots (Part II, §5.4, pp.125–126). Checked against p.126. Two columns of six plots, School A on the left and School B on the right, Classes 6, 7 and 8 in order down the page, with blue markers for the boys and orange for the girls in every grade. All twelve sit on the same 120–170 cm line. The mean is printed beside each plot and is the only number given: School A — Class 6 boys 134.8, girls 137.78; Class 7 boys 141.8, girls 141.83; Class 8 boys 149.35, girls 147.81. School B — Class 6 boys 149.84, girls 150.2; Class 7 boys 156.14, girls 155.41; Class 8 boys 156.14, girls 156.83. The individual heights are drawn as dots and are not printed anywhere, so no other summary can honestly be computed from this figure.
What the twelve means are for (Part II, §5.4, p.126). Two separate things fall out of them. Across schools, every grade in School B outruns the same grade in School A by a wide margin — the chapter prints the reader's own puzzled question about this and then does not answer it. Within schools, the boys-versus-girls comparison has no settled direction: it goes one way in some grades and the other way in others, in both schools.
The chapter's own conclusion (Part II, §5.4, p.126). In paraphrase: adults differ in height by sex in general, but a couple of schools' worth of children is not enough to settle whether boys or girls are taller across the country or the world. This is the sentence the whole topic hangs on.
The national height table (Part II, §5.4, p.127). Checked against the printed page. Average height in centimetres by age, 5 to 19, for four survey years — 1989, 1999, 2009, 2019 — with a boys' column and a girls' column inside each year. Age 5 reads 101.3 and 100.0 in 1989 and 107.1 and 107.2 in 2019; age 19 reads 163.5 and 151.9 in 1989 and 166.5 and 155.2 in 2019.
Three moments worth pausing on in that table (Part II, §5.4, p.127). (i) Boys are not taller than girls at every age: at ages 10, 11 and 12 in 2019 the girls' column runs higher, and at age 5 in 2019 it is higher by a tenth. (ii) A near-miss: fifteen-year-old boys in 2019 average 159.0 and sixteen-year-old boys in 1989 averaged 158.9. (iii) The jump between successive ages is not constant, and the biggest jump falls at a different age for boys and for girls.
The six statements to judge (Part II, §5.4, p.127). In paraphrase: that boys' and girls' averages rose at every age between 1989 and 2019; that thirteen-year-old girls in 1989 averaged more than fourteen-year-old girls in 2009; that fifteen-year-old boys in 2019 averaged more than sixteen-year-old boys in 1989; that every thirteen-year-old girl is taller than every eleven-year-old girl; that boys' averages exceed girls' at every age from 5 to 19; and that boys go on growing past 19. Two of these are settled by looking up cells, two are settled by finding a counter-example in the table, one is about individuals rather than averages, and one asks about ages the table does not cover. No answers are printed — checked against the printed page pp.127 and 128 and the end of the file — so reasoning added here must be shown as reasoning.
The country-by-country graph (Part II, §5.4, p.128). Checked against the printed page. Not a bar graph: four marker series — boys 1989, boys 2019, girls 1989, girls 2019 — plotted above a row of country names running from Timor-Leste on the left to the Netherlands on the right, with the height line labelled 145, 155, 165, 175 and 185 cm. The chapter states plainly that the line begins at 145 cm to give a closer look. With the bottom 145 cm cut away, a difference of a few centimetres occupies a large part of the picture. Both things are true at once.
A Mean Decision! (Part II, §5.4, p.129). Checked against the printed page. Two cartoons. In the first, a family has built a doorway to the family's average height and the tallest member has to stoop; in the second, two children look at a photograph of the world's tallest and shortest people standing together. Both make the same point in one image — a summary is not a specification.
Standing tall in the storm (Part II, §5.4, "Figure it Out", p.131). Checked against the printed page. A twenty-row horizontal bar chart of the cities with the most buildings over 150 m, with a value printed beside most bars but deliberately omitted for New York, Tokyo and London. Mumbai sits thirteenth in the list with 86. Three statements follow, to be judged: that exactly twelve cities have more than Mumbai; that exactly seven have fewer; and that the world's tallest building is in Hong Kong. The first two can be settled by counting rows. The third cannot be settled at all, because the chart counts buildings rather than measuring them — that is the trap, and it is the best single item in the chapter for this topic.
The animal-speed infographic (Part II, §5.3, "Figure it Out", pp.122–123). Checked against p.123, where it is printed sideways across the whole page. Fifteen creatures grouped by medium, with maximum speeds in kilometres per hour: in air, peregrine falcon 322, spine-tailed swift 170, free-tailed bat 96, green darner dragonfly 64, flying fish 56; on land, cheetah 103, pronghorn antelope 88, ostrich 64, human 37, Australian tiger beetle 8; in water, sailfish 109, dolphin 40, California sea lion 40, Gentoo penguin 35, humpback whale 26. The value line is marked at 0, 16, 32, 48, 64 and on in steps of roughly sixteen — an unusual scale worth asking about. The two questions that matter here are whether a sailfish is about four times a humpback whale's speed, which the numbers can settle, and whether a sailfish is the fastest swimmer in the world, which they cannot, because only fifteen animals are on the chart.

Figures to have open

A 2 × 6 grid of dot plots on one shared 120–170 cm line, boys and girls distinguishable by both colour and marker shape. Standard schematic; the means are given above. The individual heights are printed nowhere, so any dots drawn are illustration only.
A direction board for section 5 — six rows, one arrow each. This is the figure that carries the argument and it does not exist in the book.
The national height table, as a scrollable or highlightable data figure rather than a static image. Standard schematic, built from the printed values.
The same country-height data drawn twice, once with the value line from 0 and once from 145, so the zoom's effect is measurable. This comparison is added here; the book prints only the zoomed version.
A twenty-row horizontal bar chart of skyscraper counts with three values deliberately hidden. Redraw; the book's is a third-party infographic.
No figure needs to be taken from the textbook.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part II, printed Chapter 5, "Connecting the Dots...", §5.4 "Data Detective", pp.125–131. The named sub-headings used are "Telling Tall Tales" (pp.125–129), "A Mean Decision!" (p.129) and the "Figure it Out" that follows (pp.129–134). None carries a number.
The animal-speed infographic used in the last worked example sits in §5.3's "Figure it Out", Part II, pp.122–123.
The national height table on Part II, p.127 is described in the chapter as survey-based; no source organisation is named on the page.
Source file gegp205.pdf / gegp205.txt, printed pp.97–135; PDF page 1 is printed page 97.