Interrogating a real dataset: traffic, and rainfall

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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

Reading a line graph, its axes, its interval and its legend, and reading steepness as the size of a change — Line graphs, and what change over time looks like
The mean as a single number standing for many — The mean as the point where the distances balance
Comparing two quantities as a fraction of one another, and recognising about three quarters
Doubling, and testing whether one reading is at least twice another
Reading percentages off an axis, and knowing that shares of households need not sum across two different lines
Adding twelve readings to get an annual total
Where the west and east coasts of India are, well enough to group six named cities

What they should be able to do

State, for an unfamiliar figure, what its axes, units, interval, series and source are before interpreting anything
Ask and answer how a plotted quantity was produced from raw observations, for a launch count, a monthly average rainfall and a monthly count of rainy days
Detect that a plotted set of parts does not account for its plotted whole, and say what follows
Judge a candidate inference as supported, contradicted or simply not addressed by the figure
Explain why a claim about something absent from a figure cannot be settled by that figure
Find two consecutive years in which a plotted quantity at least doubled
Read the same axis across two figures and say what the shared scale reveals and what it compresses
Recover a missing table row by reading a plotted line, and complete a figure's title from the pattern in its data
Explain why an average curve cannot support a claim about every individual

Where it usually goes wrong

"If it is not on the graph, it did not happen." The Nepal claim is printed to catch exactly this. The figure plots three countries and a world total; everything else is outside its scope, and the correct verdict is "this figure cannot say".
"The parts of a whole must be all the parts shown." Three countries do not sum to the world figure, and the shortfall in 2024 is only about 140 objects — small enough to miss and large enough to matter.
"A rising line means it rose every year." The world line climbs steeply and still turns down at the end. Trend and monotone are different claims, and one of the printed statements confuses them.
"An average tells me about every child." The hobbies curve is the whole reason this misconception is worth a section. An average of one and a half hours is compatible with half the children playing three hours and half playing none.
"Percentages on two lines should add to a hundred." They nearly do here, and only because these two sources dominate. The caption says these are shares of households by primary source, which is what allows other sources to exist and the two lines to fall short of a hundred.
"Monthly average rainfall means the rain fell evenly through the month." It is one month's total, averaged over several years. Udupi's July figure is not a July anyone experienced; it is what July does on average.
"Two graphs drawn to the same axis are equally readable." They are equally comparable, which is not the same thing. The east-coast figure gives up three fifths of its height to make the comparison honest.
"A statement about a graph is either true or false." Three verdicts are needed: supported, contradicted, and not addressed. Two of the eight statements in this topic land in the third box, and a student who only has two boxes will force them into the wrong one.

Questions to check understanding

Given an unfamiliar figure, list its axes, units, interval, series and source before interpreting
Say how a plotted quantity was produced from raw observations, and what that leaves out
Show that a set of plotted parts does not account for a plotted whole, and state what follows
Classify each of several statements about a figure as supported, contradicted or not addressed, with a reason
Find two consecutive periods in which a quantity at least doubled
Read a value off a curve to a stated precision, and read where a curve crosses a stated level
Complete a table row from a plotted line and an annual total from a table row
Explain why an average curve cannot support a claim about every individual
Decide which of two cities is wetter on a stated measure, and note when the answer is close

Examples worth working on the board

Values marked printed appear on the page. Values marked not in the book are added readings off the printed pages and the printed page, or arithmetic added here on them. The chapter prints no answers to any exercise item and Part II has no answer appendix.

The launch figure (Part II p.119, printed). Its title gives the yearly count of objects launched into space. A subtitle says what is counted — satellites, probes and landers, crewed craft, and pieces of space-station flight hardware, whether bound for Earth orbit or beyond. Vertical axis 0 to 3,000 in five-hundreds; horizontal axis 2012 to 2024 marked every two years. Four labelled series: World, United States, China and Russia. The source line credits the United Nations Office for Outer Space Affairs, 2025.
The four series, year by year (not in the book, read off the printed page). World: about 160, 250, 265, 260, 245, 485, 455, 600, 1275, 1820, 2490, 2910, 2870 for 2012 through 2024. United States: about 60, 105, 145, 135, 110, 320, 215, 380, 1010, 1240, 1950, 2245, 2280. China: about 30 rising slowly to about 300 by 2024, passing about 90 in 2020, 145 in 2021, 225 in 2022 and 245 in 2023. Russia: between about 30 and 80 through the 2010s, reaching about 150 by 2024. The chapter itself states the last two world figures as about 2900 for 2023 and about 2800 for 2024, so the readings are anchored at the right-hand end.
The Math Talk provenance question (Part II p.119, printed, unanswered): what method could have produced this data? Not in the book: somebody has to be told about every launch and count the objects it carried, which is why the series exists at all — an international register, maintained because states report their launches. The subtitle is doing the real work here: it tells you a rideshare of forty small satellites counts as forty, not one.
The two inferences the chapter draws for you (Part II pp.119–120, printed). First: the three countries' counts do not add up to the world count, so other countries must be launching things that this figure does not show. Second: for the United States the rise from 2022 to 2023 is larger than the rise from 2023 to 2024, and you can see it in how steeply the two segments climb.
The arithmetic behind the first one (not in the book, worth showing). In 2024 the three plotted countries total about 2280 + 300 + 150 = 2730 against a world figure of about 2870 — a shortfall of roughly 140. The gap is small, which is exactly why it is a good lesson: the figure is nearly complete and still not complete.
The four candidate claims (Part II p.120, printed as a list to judge). Added verdicts:
- That the world count rose every year from 2012 to 2024 — contradicted. It falls from 2023 to 2024, and there are smaller dips at 2014 to 2015, at 2015 to 2016 and at 2017 to 2018. The book's own interpretation names the first of these — the printed bullet on Part II p.119 is the one comparing the 2024 worldwide count with the 2023 one.
- That the United States launched about three quarters of the world total in 2022 to 2024 — supported. Added readings give about 0.78, 0.77 and 0.79.
- That Nepal launched nothing between 2012 and 2024 — not addressed. Nepal is not one of the four plotted series, and a figure cannot report on what it never plotted. This is the only one of the four whose failure is about the graph's scope rather than its values.
- That China and Russia together launched about 400 objects in 2024 — roughly supported, and worth measuring carefully. Added readings give about 300 and about 150, so about 450. A class that measures and lands near 450 has done better work than one that agrees with the printed number.
The doubling question (Part II p.120, printed, unanswered). Not in the book: 2019 to 2020 runs from about 600 to about 1275, a ratio near 2.1, and clears the item's "2 times or more" bar outright. 2016 to 2017 sits right on the bar and must be handled as such: added readings put it near 220 rising to near 470, a ratio just over 2, and a reading only 20 or so higher at 2016 — well inside what this graph can be read to — pushes the ratio below 2. So do not assert it. Have the class measure that pair themselves and let the answer come out contested; that is the honest lesson of reading values off a line graph, and it is worth more here than a clean verdict. Both pairs are visible as the two steepest short climbs on the world line.
The fifty-two-bar box (Part II p.120, printed) argues for the line graph over a clustered column graph for this data. It is quoted and used in Line graphs, and what change over time looks like section 9; this topic needs it only as the reason the figure looks the way it does.
The two rainfall figures (Part II pp.120–121, printed). Both carry the same title with a blank left in it, naming monthly average rainfall along a coast the reader has to supply. Both have a vertical axis in millimetres from 0 to 900 in hundreds and the twelve months across. The first plots Kovalam with circle markers, Udupi with triangles and Mumbai with squares; the second plots Rameswaram, Chennai and Puri the same way. The source line under the second credits weather-and-climate.com.
The six series (not in the book, read off the printed page, in millimetres, January to December):
- Kovalam: 25, 45, 85, 148, 218, 297, 200, 168, 172, 260, 217, 80
- Udupi: 3, 8, 18, 50, 168, 782, 878, 605, 305, 245, 78, 18
- Mumbai: about 1, 1, 1, 3, 18, 432, 600, 430, 293, 65, 8, 2
- Rameswaram: 65, 38, 30, 73, 58, 13, 10, 20, 47, 205, 353, 200
- Chennai: 15, 10, 8, 15, 45, 75, 78, 102, 113, 218, 232, 122
- Puri: 15, 15, 15, 18, 45, 228, 365, 358, 288, 205, 55, 15 Treat every one of these as "about". They are anchored by the chapter's own descriptions of where each city peaks.
What the chapter says about them (Part II p.121, printed). The data is monthly average rainfall for six cities, built by collecting rainfall over several years and averaging each month across those years. Kovalam, Udupi and Mumbai are west-coast cities and Rameswaram, Chennai and Puri east-coast ones, and the west coast appears to receive more rain. The three west-coast cities peak between June and August. Rameswaram gets most of its rain from October to December and very little from January to September. Chennai's rain begins in June, peaks in November and runs into December. Puri, though on the east coast, peaks from July to September. January to March is dry everywhere. The section closes by sending the reader to read about the two monsoons, and a Math Talk asks for the six cities to be marked on a map.
What the shared axis does (not in the book, and the most useful thing to say about this pair of figures). Both are drawn to 900 mm, so the two are honestly comparable and the west-coast excess is visible at a glance — Udupi's July alone is larger than any month anywhere on the east-coast figure. The cost is that the east-coast figure uses only the bottom two fifths of its own height, so Chennai's and Rameswaram's very different seasons are squeezed together. Both effects come from one decision, and a class should be asked whether they would have made it.
Item 2, the rainy-days table (Part II pp.122–123, printed). Average number of days of rainfall per month:
- Mangaluru: 0.1, 0, 0.1, 1.8, 6.2, 24.1, 27.7, 24.5, 14, 8.8, 3.9, 0.9
- New Delhi: the entire row is printed blank — it is to be filled from the graph
- Port Blair: 2.4, 1.3, 0.9, 3.3, 15.5, 18.7, 17.3, 18.8, 16.8, 14.1, 11.3, 5.4
- Rameswaram: 2.6, 1.3, 1.9, 3.4, 2.5, 0.4, 1, 1, 1.9, 8.1, 10.4, 7.8 Below it is a part-drawn figure with a vertical axis of days from 0 to 30 in fives and one line already plotted; the item's part (iii) tells you that line is New Delhi's. The four tasks are: say how such data is compiled; plot the other three cities, rounding to whole days; fill the New Delhi row from the line; and name the wettest and driest city by rainy days, and the rainy season in New Delhi and in Rameswaram.
What that item works out to (not in the book). Reading the plotted line: roughly 1, 1, 1, 1, 1, 4, 10, 10, 4, 1, 0, 1 days, so New Delhi has about 35 rainy days a year. Annual totals from the printed rows: Mangaluru about 112, Port Blair about 126, Rameswaram about 42. So Port Blair has the most rainy days and New Delhi the fewest — but New Delhi and Rameswaram are within about seven days of each other, so this is an answer a class has to read carefully rather than glance at. New Delhi's rain is concentrated in July and August; Rameswaram's in October to December, which is the same contrast the chapter drew in the figures above.
Item 10, household lighting (Part II p.130, printed as two panels headed Rural and Urban). Vertical axis 0 to 100 per cent in tens; horizontal axis 1983, 1990, 2000, 2010, 2023; each panel carries a rising line labelled Electricity and a falling one labelled Kerosene. A caption states the numbers are shares of households by primary lighting energy source, and the source line credits the Household Consumer Expenditure Survey run by the National Sample Survey Office across several years. Not in the book readings: rural electricity about 15 per cent in 1983 rising to about 99 in 2023, rural kerosene about 80 falling to about 1, the two crossing near 1998 to 2000 at about 48 per cent; urban electricity about 65 per cent in 1983, about 92 by 2000 and essentially 100 by 2023, urban kerosene about 33 falling to nearly nothing.
The four statements to judge (Part II p.130, printed). Added verdicts: in 1983 most rural households did use kerosene and most urban households electricity — supported. Kerosene's share fell in both settings — supported. That in 2000 a tenth of urban households used electricity — contradicted, and instructively: about a tenth of urban households were on kerosene in 2000 while about nine tenths were on electricity, so this is a claim that read the right number off the wrong line. That there were no power cuts in 2023 — not addressed; the figure is about which source a household mainly uses, and says nothing about whether the supply was reliable.
Item 11, hours of play (Part II pp.130–131, printed). A figure whose title names the average time spent each day on hobbies and games, with one curve for Urban and one for Rural, a vertical axis marked at one hour and two hours, and ages running from about six to about twenty-four with 10, 15 and 20 labelled. Not in the book: at age 10 the urban curve reads a little over two hours and the rural a little over two and a quarter; the rural curve passes an hour and a half between ages 14 and 15, so of the offered ages 14 is the answer. Of the two claims in part (iii): fifteen-year-olds do not spend twice what ten-year-olds do — they spend rather less, about one and a quarter hours against about two — and nothing here licenses a claim about all rural fifteen-year-olds, because the curve is an average and an average tolerates any amount of variation underneath it. Beside the item sits a cartoon of children on a sofa being called outside to play, which is the chapter making the same point in one line.

Figures to have open

The launch figure (Part II p.119), redrawn from the readings above, with the subtitle and source line kept. The subtitle is load-bearing: without it "objects" is undefined.
A parts-against-whole bar for 2024: three stacked country counts against the world figure, with the unexplained remainder shaded. Not in the chapter, and it is what makes section 4 arithmetic rather than assertion.
A scope boundary figure: the four plotted series inside a frame, several unplotted countries outside it. Not in the chapter.
Both rainfall figures (Part II pp.120–121), redrawn on one shared axis so the comparison survives, plus a version of the east-coast figure rescaled to its own data for section 9's second half.
An outline map of India with the six cities marked, which the chapter's Math Talk asks for and does not supply.
The rainy-days figure (Part II p.122) with the single plotted line, so the missing row can be read off.
The two lighting panels (Part II p.130), redrawn with the crossing point marked.
The hobbies curves (Part II p.130), redrawn, plus a second panel showing several individual children scattered around the same average — the figure that kills the average-means-everyone error.

Where this sits in the book

NCERT Ganita Prakash Class 8, Part II, printed Chapter 5, "Tales by Dots and Lines", §5.2 "Visualising and Interpreting Data", Part II pp.119–121. Two unnumbered bold subheadings cover this stretch: "Space Jam", whose heading runs on into a question about traffic in the future (opening on Part II p.119 and running through the boxed argument on Part II p.120), and "Catch the (Pattern in) Rain" (Part II pp.120–121). The launch figure and the first interpretation bullets are on Part II p.119; the candidate claims, the doubling question, the box and the first rainfall figure are on Part II p.120; the second rainfall figure, the provenance answer, the coastal grouping, the peak months and the monsoon pointer are on Part II p.121.
SUMMARY, Part II p.133, fourth bullet: examining data leads to new questions and further directions to probe. That bullet is the summary of this topic and of Telling a story with data, and letting it raise the next question.
Exercise items owned by this topic: Part II pp.122–123 item 2, the rainy-days table; Part II p.130 item 10; Part II pp.130–131 item 11.
Sibling topics: the mechanics and drawing of line graphs, and the other items in both Figure it Out sets, are Line graphs, and what change over time looks like; encodings that are not graphs at all are Infographics and activity strips: what a visual shows and what it hides; the chapter's own worked data story is Telling a story with data, and letting it raise the next question.