Tales by Dots and Lines · Lesson 9 of 13
Comparing Trends and Testing Claims
“Interpret multiple lines, rainfall seasons, and claims about missing information.”
• Compare levels, changes, and contributions in multiple time series. • Distinguish a shown time window from an all-time claim. • Interpret monthly average rainfall and seasonal differences. • Classify conclusions as supported, contradicted, or not determined.
A graph can suggest a strong story: more objects are going into space, or one city has a wetter season than another. But a useful story must stay within what the data actually shows. A line rising overall may still fall in a particular year, and a country missing from the legend has not necessarily recorded zero.
In this lesson, we will read two different settings and practise careful claims. For each statement, ask whether the display supports it, contradicts it, or leaves it unanswered. The third category is valuable: “not enough information” is sometimes the most accurate conclusion.
Space Jam: A Traffic Problem in the Future?
The source display counts objects launched into space each year from 2012 to 2024. It includes a worldwide total and separate series for the United States, China, and Russia. Objects are not necessarily the same as launches of rockets: one launch can carry more than one object.
The redraw below uses approximate readings rounded to about 50 objects. It preserves the main pattern for interpretation, while exact arithmetic should use an exact table if one is available. The worldwide series includes countries that have no separate line here.
Problem
Does the graph support “The worldwide count increased every year from 2012 to 2024”?
- 1.An every-year claim requires each point to be above the preceding point.
- 2.The displayed worldwide series falls from 2017 to 2018 and again from 2023 to 2024.
- 3.One such fall is enough to contradict the claim.
- 4.A more accurate statement is that the count increased greatly overall, with some decreases within the period.
Levels, Increases, and Scope
A high point describes a large count in that year. A steep upward segment describes a large increase across that interval. When comparing steepness, use the same axes and equal time intervals; otherwise visual steepness can be misleading.
The highest point in the shown period is not automatically the highest point in history. This graph begins in 2012. It cannot by itself rule out a higher count before that year. State “highest among the years shown” unless earlier evidence is available.
Problem
Use approximate 2023 values of 2900 worldwide and 2250 for the United States. Estimate the United States share.
- 1.Divide the part by the whole: 2250 ÷ 2900 ≈ 0.776.
- 2.This is about 78%, reasonably described as roughly three quarters for a broad visual comparison.
- 3.The inputs are approximate graph readings, so a long decimal would suggest unjustified precision.
- 4.The comparison concerns objects in that year, not the cumulative number of objects ever launched.
Problem
A learner says, “Nepal has no line, so it launched no objects during these years.” Is that justified?
- 1.Check the legend: only three countries are shown separately, along with the world total.
- 2.The lack of a separate line does not state a zero count.
- 3.Other countries may contribute to the worldwide total.
- 4.The claim is not determined by this graph; it requires country-specific data.
Catch the (Pattern in) Rain
Monthly average rainfall is formed by collecting rainfall totals for the same calendar month across several years and averaging them. For example, June totals of 180, 240, and 210 mm have average 210 mm. This average describes those Junes; it is not a promise that the next June will receive exactly 210 mm.
The chapter compares Kovalam, Udupi, and Mumbai on the west coast with Rameswaram, Chennai, and Puri on the east coast. The timing of the wetter season differs. Even within the same coast, one city’s pattern need not represent all the others.
| City or group | Broad pattern shown in the chapter |
|---|---|
| Kovalam, Udupi, Mumbai | Main high-rainfall period around June–August |
| Rameswaram | Main high-rainfall period around October–December |
| Chennai | Peak around November |
| Puri | High-rainfall period around July–September |
| All six cities | Generally low rainfall around January–March |
Problem
A city receives 240, 360, 180, and 300 mm of rain in July over four years. Find the average July rainfall.
- 1.Add rainfall for the same month across the four years: 240 + 360 + 180 + 300 = 1080 mm.
- 2.Divide by the four Julys: 1080 ÷ 4 = 270 mm.
- 3.The monthly average is 270 mm for this collection of years.
- 4.The average does not mean that each July had 270 mm or that every July day had the same rainfall.
Comparing Seasonal Patterns Responsibly
A graph of six selected cities can support statements about those displayed cities. It cannot establish that every place on one coast always receives more rain than every place on the other. Broader claims require a broader and fairly chosen set of locations.
Rainfall amount and number of rainy days are also different measurements. A city can receive a large amount in a few intense showers or a similar amount spread across many days. Read the vertical unit: millimetres measure amount, while days count how often a defined rainfall condition occurred.
Rewrite Three Claims
Rewrite statements so that their scope matches the available evidence.
- Change “2023 had the most space objects ever” into a claim restricted to the plotted years.
- Change “All east-coast cities peak in November” to describe Chennai while allowing Puri’s different season.
- Change “Next July will receive 270 mm” to describe the four-year average instead.
Suitable revisions are: “2023 is the highest worldwide point among the displayed years”; “Chennai peaks around November, while Puri peaks earlier”; and “The four observed July totals have mean 270 mm.”
An overall increase is not the same as an increase every year. An omitted series is not evidence of zero. A pattern alone does not establish its cause.
Quiz
What contradicts “the count rose every year”?
A country is absent from the legend. What can we conclude about its count?
Which calculation gives a monthly average July rainfall?
Which city has its rainfall peak around November in the chapter?
Which wording matches a graph covering 2012–2024?
An every-year statement fails if even one consecutive interval decreases.
Practice Problems
- A series has values 100, 160, 150, 220 over four years. Describe its overall change and test whether it increased every year.
- Worldwide count is about 2800; three displayed countries total about 2650. What does the difference suggest?
- A series rises from 600 to 1250 in consecutive years. Has it at least doubled?
- Find the average rainfall from June totals 150, 210, 240, and 200 mm.
- A rainfall graph shows only six coastal cities. Can it establish that every west-coast place is wetter than every east-coast place?
- City A has 20 rainy days and City B has 10. Must A receive more total rainfall?
Step 1: The final value exceeds the first by 120, so it increased overall. Step 2: The decrease from 160 to 150 contradicts an every-year increase.
Key Takeaways
• Compare both values and changes; they answer different questions. • Restrict conclusions to the shown places, times, and definitions. • Missing information is different from a recorded zero. • Monthly average rainfall summarises the same month across reference years. • Use supported, contradicted, and not determined to evaluate claims.