Clustered bar graphs: comparing across categories and across time

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What to assume they know

Class 6 Ganita Prakash: reading and drawing a simple bar graph, and choosing a scale for it
Dot plots: seeing spread and clustering at a glance — a data display is a trade, and it is fair to ask what a picture gave up
The arithmetic mean as fair-share — the mean, needed for the daylight graph, which plots a monthly total divided by the days in the month
Multiplying and dividing by 5, 20 and 1000 to read values off a scale
Reading a table with twelve columns

What they should be able to do

Read a value off a clustered column graph by referring to the markings on the vertical line
State the scale of a graph, and use it to estimate a bar that falls between two markings
Explain what the clustered form buys over two separate graphs of the same data
Say when reordering the categories changes the meaning of a graph and when it does not
Apply the chapter's two-step routine — first identify what is given, then infer from it
Distinguish a value read off the graph from an estimate, and say which you are giving
Choose a scale and draw a clustered graph from a table
Explain why a pattern fill as well as a colour is used to tell two series apart

Where it usually goes wrong

"Any two graphs of the same thing can be compared." Only if they share a scale, and even then the eye is unreliable across a page break. The chapter's p.114 pair is drawn on identical scales and is still hard to use, which is the honest version of the argument.
"A cluster of bars adds up to something." It does not. Two bars in one cluster are two separate measurements of the same category, not parts of a whole. This is the error a stacked bar chart invites and a clustered one must not.
"Reading a value off a graph gives you the value." It gives an estimate whose precision is set by the markings. The rocket graph's "perhaps 61" is the chapter modelling exactly this.
"You can always reorder the bars to make a graph tidier." Sorting the months of the year by price would destroy the seasonal pattern that is the whole reason for plotting them. Sorting the organisations loses nothing. The test is whether the category order is itself data.
"Colour is enough to tell two series apart." The chapter adds hatching and dots and says why: some readers cannot separate the colours, and greyscale printing removes them for everyone.
"A graph shows the numbers in the table." The daylight graph does not — it shows monthly totals divided by the days in the month. Always ask what quantity a bar's height actually is.
"If a graph has no numbers printed on it, it is a bad graph." The rocket graph is deliberately number-free and the chapter uses it to teach estimating. What makes a graph unreadable is a missing scale, not missing labels.

Questions to check understanding

Read a stated value off a clustered graph, and estimate one that falls between two markings
State the scale of a given graph
Draw a clustered graph from a table, choosing and stating a scale — the chapter's own practice items at Part II, §5.3, pp.124–125 supply three such tables, of which items 2 and 3 are drawn from scratch
Judge whether a list of statements is supported by a given graph
"How many more / how many times as many?" comparisons between two bars of one cluster or two clusters
Describe a trend across the bars of one series, in words
Explain why a particular graph's categories may or may not be reordered
Complete a partly-drawn graph from a table — the electric-vehicle item at Part II, §5.3, pp.124–125 leaves two states' clusters blank on purpose

Examples worth working on the board

The onion table, again (Part II, §5.3, p.114). Monthly price in rupees per kilogram, January to December. Yahapur: 25, 24, 26, 28, 30, 35, 39, 43, 49, 56, 59, 44. Wahapur: 19, 17, 23, 30, 38, 35, 42, 39, 53, 60, 52, 42. The same twelve pairs that were a dot plot in §5.2 become a clustered graph here; put the two pictures of one data set side by side at some point in the explanation.
The two separate column graphs (Part II, §5.3, p.114). Checked against the printed page. Two full-width graphs, one per town, stacked with identical vertical scales running 0 to 60. They are printed unlabelled by series because each graph holds only one. This is the "before" of the whole section.
The clustered version (Part II, §5.3, p.115). Checked against the printed page. Twelve clusters of two bars, blue for Yahapur and red for Wahapur, with a legend at the top right and the vertical line labelled in rupees. Labels appear at 0, 10, 20, 30, 40, 50 and 60 with a faint rule at every intervening 5. The blue bars carry diagonal hatching and the red bars carry dots — the chapter says outright that this is so the two can be told apart without colour. Reproduce that redundancy in an added graph.
The rocket-launch graph (Part II, §5.3, p.116). Checked against the printed page. A ten-row horizontal-bar graph, three bars per row for 2021, 2022 and 2023, credited on the artwork to Bryce Tech and sourced by the chapter to a Statista chart counting rocket launches worldwide, company by company and agency by agency. The rows, top to bottom, are SpaceX, CASC, Roscosmos, Arianespace, Rocket Lab, United Launch Alliance, ISRO, Galactic Energy, Expace, and a final row labelled Other; each carries a national flag. The value line runs 0 to 100 with markings only every 20 — which is why the boy in the margin wishes for guidelines at 5, 10 and 15. The chapter states the scale as one unit of length to twenty rockets. No numeric values are printed on the bars, checked on the printed page; everything about this graph is read by estimation, and that is what it is there to teach.
The annotated version (Part II, §5.3, p.117). Checked against the printed page. The same graph redrawn with five annotations pointing into it — one reading a bar as perhaps 61, one describing a row that rises year on year with the second bar about twice the first, one describing a row that falls with the third bar about half the second, one describing a rise then a fall, and one estimating the bottom row's 2023 value at around 25.
The six statements to be judged (Part II, §5.3, pp.117–118). In paraphrase, the reader is asked which of these the graph supports: that every organisation launched more than it had the year before; that only a United States organisation passed fifty launches in a single year; that France's three-year total is under forty; that one Chinese organisation's three-year average is around forty; that ISRO out-launched Galactic Energy over the three years; and that Russia passed sixty over the three years. Two further open questions follow — which organisations rose every single year, and which band the 2023 worldwide total falls into, with four bands offered. None is answered in print.
The daylight tables (Part II, §5.3, p.118). Monthly hours, January to December. City 1: 210, 257, 372, 441, 536, 564, 555, 465, 394, 310, 222, 186. City 2: 459, 384, 381, 327, 304, 276, 295, 318, 369, 409, 435, 468. The graph on p.119 plots each of these divided by however many days that month has.
The daylight graph (Part II, §5.3, p.119). Checked against the printed page. Twelve clusters of two bars, orange for City 1 and blue for City 2, vertical line labelled 0, 5, 10, 15, 20 with the stated scale of one unit to five hours. Note for whoever writes the explanation: the graph's own printed title says sunshine where the surrounding text says daylight, and the text's stated maximum for City 1 of about 17 to 18 hours is a shade under what the table gives — 564 hours over 30 days is 18.8. Use the tables, state the division, and let the computed value stand.
The reveal (Part II, §5.3, p.120). Inputs: City 1 turns out to be Helsinki in Finland, and City 2 to be Wellington in New Zealand; the two sit in opposite hemispheres, far from the Equator, which is why one peaks in June while the other bottoms out. A world map with a pin on each is printed on the same page. The chapter also offers June daylight in City 1 as roughly three-quarters of the 24-hour day and December–January as roughly a quarter — good round numbers to check against the tables.
The cricket over-by-over graph (Part II, §5.3, p.122). Checked against the printed page. Twenty clusters of two bars, one per over, blue for one team and red for the other, vertical line running 0 to 15 with the stated scale of one unit to five runs. A small circle drawn above a bar means a wicket went down during that over. Four questions follow, all unanswered in print: who batted first and who won; how many runs the blue team took in over 12; in which over the red team scored least; and whether the target set by the side batting first can be read off at all.

Figures to have open

The two single-town column graphs, then the clustered version, built from the same twelve pairs. Standard schematic; this must be a movement rather than three static pictures, because the argument is the merge.
A greyscale rendering of the clustered graph, to prove the hatching works.
A horizontal clustered bar graph with ten rows and three bars per row, with a value line marked only every twenty units. Redraw; the book's is a third-party chart credited to Bryce Tech and should not be reproduced.
The daylight graph, drawn from the computed per-day values rather than from the monthly totals, so the division is visible.
A world map with two pins, one in northern Europe and one in the south-west Pacific, and the Equator drawn. Standard schematic.
An over-by-over cricket graph with wicket markers.
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...", §5.3 "Visualising Data", pp.114–125. The named sub-headings used are "Clubbing the Columns" (pp.114–115), "10…9…8…7…6…5…4…3…2…1…Take Off!" (pp.115–118), "Summer and Winter at the Same Time" (pp.118–121), "All it Takes is a Minute" (pp.121–122) and the "Figure it Out" that closes the section (pp.122–125). None carries a number; this book prints one level of section numbering only.
The SUMMARY's line on clustered bar graphs: Part II, p.134.
The rocket graph's own source line, printed under it on Part II, p.116: a Statista chart counting rocket launches worldwide, company by company and agency by agency, with the artwork itself credited to Bryce Tech.
Source file gegp205.pdf / gegp205.txt, printed pp.97–135; PDF page 1 is printed page 97.