Telling a story with data, and letting it raise the next question

What to assume they know

• Reading a line graph, its axes and its scale, and knowing that the marks are the data and the line joins them — Line graphs, and what change over time looks like
• Judging what a figure does and does not support — Interrogating a real dataset: traffic, and rainfall
• Mean and median, and computing both from a collected data set — The mean as the point where the distances balance, Whether adding a value raises or lowers the median, Mean and median from a frequency table, by hand and in a spreadsheet
• Reading a pie chart, and the animal sleep-time chart from earlier in Part II — Building a pie chart: turning counts into angles
• Reading a zoomed axis: knowing that an axis need not start at zero and what changes when it does not
• Adding times in hours and half hours

What they should be able to do

• Describe the shape of a curve in words, naming where it falls, flattens and rises
• Read stated values off a curve at given ages, to the precision the axis supports
• Explain why hundreds of closely spaced points look like a smooth curve, and why a column graph of the same data would be unreadable
• Compare a full-scale panel with a zoomed panel of the same data, and say what each is good for
• Separate the claims a curve of averages supports from the claims it cannot
• Turn a "why" question raised by a figure into a statement of what data would answer it
• Design a small collection: what to record, from whom, for how long, and with what definition of the quantity
• Summarise collected data with a mean and a median for each of several groups, and say what each summary adds
• Say what the next figure should show, given what the last one raised

Where it usually goes wrong

• "A data story should end with an answer." This one ends with three questions, and the SUMMARY endorses that. Ending on a question is not a failure to conclude; it is what a finding looks like before the next collection.
• "A smooth curve means the quantity varies smoothly." It means the points are close together. The data is still one value per age; the smoothness is a drawing effect, and the chapter says so.
• "The zoomed panel exaggerates." Both panels are the same data. The full-scale panel understates the dip as surely as the zoomed one dramatises it, and the reason to print both is that neither is sufficient alone.
• "The curve says people sleep less as they get older." It says people of different ages reported different amounts at one time. Following one person for sixty years is a different study, and it might not give this shape.
• "So the average person sleeps eight hours — that is how much sleep I need." The text's seven-to-nine band is about the range across individuals; the curve's eight hours is a middle of that range. Neither is a prescription for anybody, and the paragraph before the figure lists the reasons an individual's need differs.
• "The graph covers all ages." It runs from 6 to 75. Newborns, whom the closing question is about, are outside it, which is exactly why the question has to be asked rather than read off.
• "Collecting data is the easy part." The group project makes the difficulty concrete: two groups that disagree about whether naps count have collected two different quantities and cannot pool them.
• "An interesting question is a good question." A good question here is one that names the data that would settle it. Section 11 should convert each of the three into a sentence of the form "we would need to record …".

Questions to check understanding

• Describe the shape of a given curve in words, naming where it falls, flattens and rises
• Read values off a curve at stated points and state the precision the axis allows
• Explain why a line graph was chosen over a column graph for a data set with dozens of points
• Given a full-scale and a zoomed version of one figure, say what each is suited to
• Sort several statements about a figure into supported and unsupported, with reasons
• Rewrite a "why" question as a statement of the data that would answer it
• Design a data collection for a stated question, including the definition of what is being measured
• Compute a mean and a median for each of several groups from collected data and compare them
• Propose what the next figure should show, given the last one's findings

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, or reasoning added here on them. The chapter prints no answers to any of the questions in this subsection and Part II has no answer appendix.

• The opening (Part II p.126, printed). The subsection begins by asking the reader to remember the pie chart of sleeping times from the proportionality chapter, then states that some animals sleep as little as two hours a day and some as much as twenty, wonders aloud whether insects sleep, says that humans typically sleep about seven to nine hours, and notes that how much sleep a person needs depends on age, living conditions and lifestyle — the food they eat, the activities they do — among other things, and that babies sleep longer than adults. Every one of those is a claim the graph will not test, and listing them first is what makes the rest a story rather than a figure.
• The two panels (Part II p.126, printed). Both are titled for night sleep across ages and both carry a vertical axis labelled in hours per day and a horizontal axis labelled in years. The left panel runs 0 to 12 on the vertical axis with ages marked at 10, 30, 50 and 70; the right panel is the same curve over 7.0 to 12.0 in half-hour steps with ages marked every ten years, and the page says in as many words that it is a zoomed version of the first. A source line under the pair credits the National Time Use Survey, 2024.
• The curve (not in the book, read off the printed page). It starts near 9.6 hours at the left-hand end, falls steeply through the teens, is down to about 8.5 by age 20 and about 8.2 by 30, bottoms out around 8.05 near age 40, and lifts steadily to about 8.7 at the right-hand end. The chapter's own readings for the same curve are about 9.5 hours at age 6, about 8 hours between 30 and 50, and about 8.5 hours after 50 — so the shape above is anchored by the book at three points.
• What the chapter says about the drawing (Part II p.127, printed). The earlier figures are a few joined segments; this one reads as a smooth curve, because 80 points sit so close together that the joins disappear. Drawn as columns the same data would need 70 of them and would come out cluttered and heavy, where the line is light and shows the pattern.
• The count worth checking (not in the book). The page introduces the figure as covering ages 6 to 75, which is 70 ages, and then says 80 points and 70 columns. Two of those three numbers agree and one does not. Nothing in the mathematics depends on it, and a class that notices deserves to be told they are right — the useful version of the sentence is that there are dozens of points, one per age, and that is why the segments disappear.
• What the two panels are each for (not in the book, and the most transferable point in the topic). On the full-scale panel the whole variation from 8 to 9.6 hours occupies about an eighth of the height, so the honest impression is that sleep barely changes across a lifetime. On the zoomed panel the same variation is about 2.4× larger — the right-hand panel runs 7.0 to 12.0 hours in half-hour steps against the left panel's 0 to 12 — which is enough to make the dip and the post-fifty lift legible. It does not fill the frame: the plotted range occupies roughly three tenths of the zoomed panel's height, leaving about two and a half hours of empty headroom above the curve. Say the zoom factor rather than implying the panel is full, or the honest point about axes turns into the exaggeration it is warning against. Neither panel lies; each answers a different question, and printing both is the fair way to show a small variation. This is the chapter's own answer to the worry a reader should have about any zoomed axis.
• Claims the curve supports (not in the book): that average sleep falls from childhood into middle life; that the fall is steepest in the teens; that the middle-life level is close to eight hours; that the trend turns upward after about fifty; and that the whole range of variation across sixty-nine years is well under two hours.
• Claims it cannot support (not in the book): that any particular person sleeps that long; that the seven-to-nine-hour band mentioned in the text is wrong or right, since that band is about individuals and this curve is about averages; that ageing causes the change, since a survey taken at one moment compares different people rather than following anyone; that newborns sleep longest, since the figure starts at 6; and anything at all about insects, other countries or other species. Each of the chapter's three closing questions falls into this box, which is why they are questions.
• The three closing questions (Part II p.127, printed, unanswered): why newborns and infants sleep for so long; whether people in different countries sleep differently; and whether animals show similar patterns across their own ages. Together with the two reader bubbles on Part II p.125 — one asking what the rice-preferring and wheat-preferring states have in common, the other whether the preferences were the same a century ago — these are the chapter's model of what a good response to a figure looks like.
• Item 13, part (i) (Part II p.131, printed as a small-group project for three or four students). Track the daily sleep of every family member for a week, counting night sleep, naps and any other daytime sleep; show each person's data on strips; pool the group's data and compute the mean and median sleep time for children, for adults and for the elderly; share what you find. Not in the book: the definition given in the item — that naps count — is the most important sentence in it, because a group that defines the quantity differently from the next group cannot pool anything. Three groups, three medians, and a comparison with the chapter's curve is the shape of a real answer.
• Item 13, part (ii) (Part II p.131, printed). Find out when schools start and end for Class 8 across several schools anywhere in the country, asking neighbours, relatives, parents and friends; the item gives Manoj's own school as running from half past nine to half past four, seven hours including class time and breaks; then analyse and present the data. Not in the book: this is the same collection problem with a much cleaner quantity, and the presentation it invites is a line graph or a dot plot of school-day lengths, which loops the project back to Line graphs, and what change over time looks like.
• The chapter's own last word (Part II p.133, printed as the fourth SUMMARY bullet): looking hard at data throws up fresh questions and fresh lines worth following. That single bullet is the thesis of this topic in the book's own accounting.

Figures to have open

• The two sleep panels (Part II p.126), redrawn from the readings above with both axes labelled and the source line kept. Section 5 fails without both panels.
• A crowding figure: the same underlying curve drawn with 7 points, then 20, then 70, so that the smoothness is seen to arrive. Not in the chapter, and it is what makes section 3 more than a restatement.
• A claims table with two columns, supported and not supported, each row carrying its reason. Not in the chapter.
• A collection-design card for the group project: what to record, from whom, for how long, and the definition of sleep the item supplies. Standard schematic.
• A pooled-results panel: three groups' strips reduced to a mean and a median for each of three age bands.
• The animal sleep pie chart can be recalled as a thumbnail; it belongs to Building a pie chart: turning counts into angles and should not be re-taught here.
• No photograph is needed.

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", the unnumbered subsection "Data Story: Sleepy-Deepy", Part II pp.126–127. The opening paragraphs and the two panels are on Part II p.126; the discussion of why the curve looks smooth, the three read-off values and the three closing questions are at the top of Part II p.127, immediately above the chapter's last Figure it Out.
• The two reader bubbles are printed at the top of Part II p.125, responding to the infographic on the facing page; the figure itself belongs to Infographics and activity strips: what a visual shows and what it hides.
• SUMMARY, Part II p.133, fourth bullet, is the chapter's own statement of this topic's thesis.
• Exercise item owned by this topic: Part II p.131 item 13, both parts.
• Backward pointer inside this unit: the animal sleep-time chart the subsection opens by recalling is in Part II printed Chapter 3 and is covered by Building a pie chart: turning counts into angles.
• Sibling topics: Line graphs, and what change over time looks like for the line-graph mechanics this figure assumes, Interrogating a real dataset: traffic, and rainfall for the habit of testing candidate claims, and Infographics and activity strips: what a visual shows and what it hides for the strips the group project asks students to draw.