Tales by Dots and Lines · Lesson 12 of 13
Data Stories Across Time
“Interpret sleep and household data, compare clock times, and design a small investigation.”
• Explain how a vertical scale changes the visual impression of a trend. • Distinguish a group average or household proportion from an individual claim. • Calculate durations using clock times, including intervals across midnight. • Plan a fair, clearly labelled data investigation.
The same dataset can tell a different-looking story when its axis is enlarged. A small change may look dramatic in a close-up view and almost flat on a full scale. Neither picture should be read without its labels.
This lesson connects several data stories from the chapter: sleep at different ages, changing household lighting, time spent on hobbies, sunrise and sunset, and moonrise and moonset. The common skill is to identify exactly what was measured before making a claim about people or time.
Data Story: Sleepy-Deepy
The source graph summarises average daily sleep duration across ages. Its broad pattern starts at about 9.5 hours around age 6, falls towards about 8 hours during ages 30–50, and then rises towards about 8.5 hours at older ages. These are observations about the displayed population, not personal sleep instructions.
The two redraws below use the same approximate age points. The first begins its vertical axis at zero; the second shows only the range 7–12 hours. The second makes smaller changes easier to see, but the values themselves have not changed. The redraw samples a few ages rather than reproducing every point of the source’s smooth curve.
Problem
The displayed average changes from about 9.5 to 8 hours. Calculate the change and explain the effect of zooming.
- 1.Subtract the later value from the earlier: 9.5 − 8 = 1.5 hours.
- 2.Convert 1.5 hours to 90 minutes if useful.
- 3.A vertical axis starting at 7 spreads this difference over more of the plotting height.
- 4.The visual drop looks larger, but the numerical change remains 1.5 hours in both charts.
Averages Describe Groups
An average of 1 hour spent on hobbies does not mean every child spends at least 1 hour. Two values, 0 and 2 hours, already have mean 1 hour. An average does not supply the minimum, maximum, or the time of any named child.
The chapter’s hobbies-and-games display compares age groups in rural and urban areas. It shows lower average durations at older displayed ages. This does not by itself follow the same children as they grow up, establish the reason for the pattern, or prove that every child follows it.
Problem
A group of children has mean hobby time 1.5 hours. Must each child spend at least 1 hour on hobbies?
- 1.Try a two-child dataset: 0.5 hour and 2.5 hours.
- 2.Their total is 3 hours and their mean is 3 ÷ 2 = 1.5 hours.
- 3.One child spends less than 1 hour, so the proposed claim is false.
- 4.To determine a minimum, we need individual observations or a distribution that supplies it.
Household Lighting and What It Does Not Tell Us
The chapter’s household-lighting graphs compare the proportions using electricity or kerosene as their primary lighting source across several decades. Electricity’s share rises and kerosene’s share falls in both rural and urban data. In the early displayed period, kerosene dominates the rural graph while electricity dominates the urban graph.
Primary lighting source means the main source a household reports using. It is not a measurement of uninterrupted supply. Even if nearly all households report electricity as primary, there can still be power cuts. Also, a percentage of households is not automatically the same as a percentage of people, because household sizes vary.
| Claim | What the measure allows |
|---|---|
| Electricity becomes more common as the primary source | Supported by an increasing electricity-share series |
| Every household has electricity for every hour | Not determined by primary-source shares |
| Kerosene’s share falls over the displayed period | Supported by the falling kerosene series |
| The electricity percentage is a count of households | A percentage needs the total household count to become a count |
Problem
In an illustrative survey of 400 households, 90% report electricity as their primary lighting source. What count does that represent, and does it prove there were no outages?
- 1.Convert 90% to 0.9.
- 2.Multiply by the total: 0.9 × 400 = 360 households.
- 3.This gives the number reporting electricity as primary.
- 4.It provides no outage duration or frequency, so it cannot prove uninterrupted electricity.
Sunrise, Sunset, and Day Length
A sunrise–sunset graph contains two time series for each location. The morning-time series is sunrise, while the evening-time series is sunset. Day length is the elapsed time from sunrise to sunset on the same date. A later sunset alone does not guarantee a longer day if sunrise is later too.
Convert clock times to minutes after midnight before subtracting when the arithmetic is awkward. Remember that 06:30 is 6 hours 30 minutes, or 6.5 hours. It is not 6.30 hours, since an hour contains 60 minutes rather than 100.
Among these displayed January records, Kibithu has the earliest sunrise, near 06:00. Its sunset is near 16:30, giving roughly 10.5 hours of daylight. Around June, Srinagar’s sunrise near 05:15 and sunset near 19:45 give about 14.5 hours, the longest peak day length among these displayed locations. These are approximate readings of the supplied graph, not exact times for a chosen date.
| Illustrative location and month | Sunrise | Sunset | Day length |
|---|---|---|---|
| Location A, January | 06:40 | 17:40 | 11 h |
| Location A, June | 05:30 | 19:00 | 13 h 30 min |
| Location B, January | 06:20 | 18:10 | 11 h 50 min |
| Location B, June | 06:00 | 18:40 | 12 h 40 min |
Problem
Compare the two June day lengths in the illustrative table.
- 1.For Location A, 19:00 − 05:30 = 13 hours 30 minutes.
- 2.For Location B, 18:40 − 06:00 = 12 hours 40 minutes.
- 3.Convert to minutes: 810 and 760.
- 4.Location A has 50 minutes more daylight in these example records. These are teaching examples, not measurements for named cities.
When a Clock Graph Crosses Midnight
Clock-time data wraps around at midnight. A moonrise near 23:40 followed on a later date by one near 00:30 may appear to jump down a clock-time graph. That visual jump can reflect the clock restarting at zero, not a sudden reversal of the underlying pattern.
Read the legend carefully to distinguish moonrise from moonset and inspect dates as well as times. A moon that rises near sunset and sets near sunrise suggests a full-moon period; rising and setting near the Sun suggests a new-moon period. These are approximate clues. Precise phase dates need the date, place, and appropriate astronomical information.
In the supplied pattern, moonrise is near 18:00 and moonset near 06:00 around the 13th–14th, suggesting the full-moon period. Near the 28th–29th, moonrise is around sunrise and moonset around sunset, suggesting the new-moon period. The graph alone supports approximate dates, not an exact phase time.
Problem
An observation period begins at 23:40 and ends at 00:30 the following day. How long does it last?
- 1.From 23:40 to midnight is 20 minutes.
- 2.From midnight to 00:30 is 30 minutes.
- 3.The total duration is 20 + 30 = 50 minutes.
- 4.Subtracting 23.40 from 0.30 as decimal numbers would mix up clock notation and the change of date.
Designing a Small Data Story
A useful investigation starts with a question you can answer using the data you can collect. You might compare daily activity durations across a week, total daily sleep for different age groups in a small household sample, or school start and finish times. Define the measure before collecting values.
For sleep duration, include naps if the question concerns total daily sleep, and use the same rule for everyone. For school duration, decide whether breaks are included. If one person contributes seven days and another only one, pooling every record gives the first person more weight. You can instead calculate each person’s weekly mean and clearly describe what is being averaged.
Plan, Collect, Check, Explain
Choose a small project about activity time or school schedules.
- Write one clear question and define the unit and observation period.
- Collect only the necessary values, using labels such as Person A if names are unnecessary.
- Check impossible totals, missing days, and inconsistent time formats.
- Choose a table, strip, or line graph to match your question.
- Calculate a useful summary, write two supported findings, and state one limitation.
A small convenience sample can reveal a pattern worth exploring, but it does not represent every child, household, or school. Good reporting makes the sample and its limitations visible.
Quiz
Two graphs use the same data but different vertical ranges. What stays the same?
A mean of 1 hour of hobby time proves what about every individual?
What is the duration from 06:25 to 18:10 on the same day?
What is the duration from 23:50 to 00:20 the next day?
A high electricity-primary-source percentage proves that there were no power cuts. How should this claim be classified?
Changing an axis scale changes visual size, not the underlying values.
Practice Problems
- An average sleep value changes from 8.2 to 8.5 hours. Express the increase in minutes.
- Give three hobby-time values with mean 1 hour but one value below 30 minutes.
- Sunrise is 05:45 and sunset is 18:20. Find the day length.
- A school day runs from 09:30 to 16:30, including two breaks totalling 50 minutes. Find the full duration and time outside breaks.
- In an illustrative survey, 72% of 250 households use electricity as primary lighting. Find the number.
- Person A records sleep for seven days, but Person B records only one day. What must you consider before comparing them?
Step 1: The increase is 8.5 − 8.2 = 0.3 hour. Step 2: Multiply by 60: 0.3 × 60 = 18 minutes. Step 3: Decimal hours are not read as clock minutes.
Key Takeaways
• Read the vertical scale before judging how large a change looks. • Group averages do not specify every individual’s value. • Primary-source proportions do not measure service reliability. • For clock arithmetic, use hours and minutes carefully and track midnight. • A data story needs a clear question, consistent definitions, and conclusions that fit the sample.