Integration of Ideas · Lesson 5

What the data can and can't support

When a passage comes with a table or graph, some questions ask which claim the figure supports, and others ask which claim goes too far. Either way, you aren't judging whether a claim is sensible or likely. You're judging whether the data alone back it.

Put four questions to the figure. Does it measure that? Table 1 below records how students traveled, not what they prefer or would do. For whom? Only the 400 students who answered, in four distance groups. When? One week in October. Does it show a cause? It shows that walking and biking fall as distance grows, but a table of percents can't show why.

A claim that fails any one of the four goes beyond the figure, even if the author believes it and even if it's probably true. Claims that pass name a row and a column you can point to.

How Cedar Ridge Gets to School

This passage is from a student newspaper column about a school travel survey.

1Each fall, the student newspaper at Cedar Ridge High School runs a short survey about how students get to school. This year, 400 students answered during the second week of October. They reported how they traveled on the morning of the survey and roughly how far they live from campus. Students who used more than one way of traveling, such as walking to a friend's car, were asked to choose the one that covered most of the trip. Table 1 groups their answers by distance.

2The results will not surprise anyone who has watched the front drive at 7:45. Walking and biking are common among students who live close to school and almost disappear farther out, where the bus takes over. Cars carry about a quarter of the students who live under a kilometer away and a larger share of everyone else.

3Still, I think the numbers hide an opportunity. Seventy percent of students who live under one kilometer away walk or bike, but only thirty percent of those living one to three kilometers away do. A three-kilometer ride takes about twelve minutes on a bicycle, hardly a hardship. In conversations for this article, several students in that middle group told me they would ride if they had somewhere safe to leave a bike. The school's only rack sits uncovered beside the loading dock, and on rainy days it stays nearly empty.

4A covered, well-lit bike shelter near the main entrance would cost far less than another bus route, and I believe it would move dozens of students out of cars. It would also shorten the line of cars that backs up onto Linden Road each morning, a line that some neighbors have complained about to the school board.

5The survey has limits, and readers should keep them in mind. It describes one week in October, when the weather was mild. It counts only students who chose to answer. And it records how students traveled, not why. A rainy week in February might look quite different, and so might the answers of students who skipped the survey. Even so, it is a better starting point than guesswork, and it points toward a shelter.

Table 1
Distance from schoolStudents surveyedWalk or bike (%)Bus (%)Car (%)
Under 1 km8070525
1–3 km140303535
3–5 km11085240
Over 5 km7006040
Table 1 groups the 400 students surveyed by distance from school and gives the percent who walked or biked, rode the bus, or came by car. Under 1 km (80 students): 70, 5 and 25 percent. 1–3 km (140 students): 30, 35 and 35. 3–5 km (110 students): 8, 52 and 40. Over 5 km (70 students): 0, 60 and 40. Walking and biking fall as distance grows, and the bus share rises.

Worked example Easy

Show the whole passage

How Cedar Ridge Gets to School

This passage is from a student newspaper column about a school travel survey.

1Each fall, the student newspaper at Cedar Ridge High School runs a short survey about how students get to school. This year, 400 students answered during the second week of October. They reported how they traveled on the morning of the survey and roughly how far they live from campus. Students who used more than one way of traveling, such as walking to a friend's car, were asked to choose the one that covered most of the trip. Table 1 groups their answers by distance.

2The results will not surprise anyone who has watched the front drive at 7:45. Walking and biking are common among students who live close to school and almost disappear farther out, where the bus takes over. Cars carry about a quarter of the students who live under a kilometer away and a larger share of everyone else.

3Still, I think the numbers hide an opportunity. Seventy percent of students who live under one kilometer away walk or bike, but only thirty percent of those living one to three kilometers away do. A three-kilometer ride takes about twelve minutes on a bicycle, hardly a hardship. In conversations for this article, several students in that middle group told me they would ride if they had somewhere safe to leave a bike. The school's only rack sits uncovered beside the loading dock, and on rainy days it stays nearly empty.

4A covered, well-lit bike shelter near the main entrance would cost far less than another bus route, and I believe it would move dozens of students out of cars. It would also shorten the line of cars that backs up onto Linden Road each morning, a line that some neighbors have complained about to the school board.

5The survey has limits, and readers should keep them in mind. It describes one week in October, when the weather was mild. It counts only students who chose to answer. And it records how students traveled, not why. A rainy week in February might look quite different, and so might the answers of students who skipped the survey. Even so, it is a better starting point than guesswork, and it points toward a shelter.

Table 1
Distance from schoolStudents surveyedWalk or bike (%)Bus (%)Car (%)
Under 1 km8070525
1–3 km140303535
3–5 km11085240
Over 5 km7006040
Table 1 groups the 400 students surveyed by distance from school and gives the percent who walked or biked, rode the bus, or came by car. Under 1 km (80 students): 70, 5 and 25 percent. 1–3 km (140 students): 30, 35 and 35. 3–5 km (110 students): 8, 52 and 40. Over 5 km (70 students): 0, 60 and 40. Walking and biking fall as distance grows, and the bus share rises.

Which claim is directly supported by the data in Table 1?

  1. Most of the surveyed students living under 1 km from school came by car.
  2. None of the surveyed students living over 5 km from school walked or biked.Answer
  3. Most of the surveyed students living 1–3 km from school rode the bus.
  4. Students living 3–5 km from school chose the bus because they found it faster.

How to solve it

  1. Name the row and the column each choice needs.
  2. Read the cell: over 5 km, walk or bike, 0 percent. That matches B.
  3. Reject any choice that needs a reason or a feeling. The table holds only percents.

Why each choice is right or wrong

  • A. Incorrect. In the under 1 km row the car share is 25 percent. The largest share there, 70 percent, walked or biked.
  • B. Correct. In the over 5 km row the walk or bike column reads 0 percent, so none of those 70 surveyed students walked or biked.
  • C. Incorrect. In the 1–3 km row the bus share is 35 percent, not a majority. The car share is also 35 percent and walk or bike is 30 percent.
  • D. Incorrect. Table 1 shows how students traveled, not why. The passage itself says the survey “records how students traveled, not why.”

Worked example Medium

Show the whole passage

How Cedar Ridge Gets to School

This passage is from a student newspaper column about a school travel survey.

1Each fall, the student newspaper at Cedar Ridge High School runs a short survey about how students get to school. This year, 400 students answered during the second week of October. They reported how they traveled on the morning of the survey and roughly how far they live from campus. Students who used more than one way of traveling, such as walking to a friend's car, were asked to choose the one that covered most of the trip. Table 1 groups their answers by distance.

2The results will not surprise anyone who has watched the front drive at 7:45. Walking and biking are common among students who live close to school and almost disappear farther out, where the bus takes over. Cars carry about a quarter of the students who live under a kilometer away and a larger share of everyone else.

3Still, I think the numbers hide an opportunity. Seventy percent of students who live under one kilometer away walk or bike, but only thirty percent of those living one to three kilometers away do. A three-kilometer ride takes about twelve minutes on a bicycle, hardly a hardship. In conversations for this article, several students in that middle group told me they would ride if they had somewhere safe to leave a bike. The school's only rack sits uncovered beside the loading dock, and on rainy days it stays nearly empty.

4A covered, well-lit bike shelter near the main entrance would cost far less than another bus route, and I believe it would move dozens of students out of cars. It would also shorten the line of cars that backs up onto Linden Road each morning, a line that some neighbors have complained about to the school board.

5The survey has limits, and readers should keep them in mind. It describes one week in October, when the weather was mild. It counts only students who chose to answer. And it records how students traveled, not why. A rainy week in February might look quite different, and so might the answers of students who skipped the survey. Even so, it is a better starting point than guesswork, and it points toward a shelter.

Table 1
Distance from schoolStudents surveyedWalk or bike (%)Bus (%)Car (%)
Under 1 km8070525
1–3 km140303535
3–5 km11085240
Over 5 km7006040
Table 1 groups the 400 students surveyed by distance from school and gives the percent who walked or biked, rode the bus, or came by car. Under 1 km (80 students): 70, 5 and 25 percent. 1–3 km (140 students): 30, 35 and 35. 3–5 km (110 students): 8, 52 and 40. Over 5 km (70 students): 0, 60 and 40. Walking and biking fall as distance grows, and the bus share rises.

Which claim goes beyond what Table 1 can support?

  1. A smaller share of the 1–3 km group walked or biked than of the under 1 km group.
  2. The 1–3 km group had more surveyed students than any other distance group.
  3. The car share was the same for the 3–5 km group and the over 5 km group.
  4. A covered bike shelter would get more of the 1–3 km group to bike to school.Answer

How to solve it

  1. Run each claim through the four questions: what is measured, for whom, when, and is a cause claimed?
  2. A, B and C each point to cells you can read: 30 against 70, 140 as the largest count, 40 and 40.
  3. D predicts what would happen after a change. No column measures that, so it goes beyond the table.

Why each choice is right or wrong

  • A. Incorrect. Supported: the walk or bike column reads 30 percent for 1–3 km and 70 percent for under 1 km.
  • B. Incorrect. Supported: the students surveyed column reads 140 for 1–3 km, more than 80, 110 or 70.
  • C. Incorrect. Supported: the car column reads 40 percent in both the 3–5 km row and the over 5 km row.
  • D. Correct. This predicts the effect of a change the survey never tested, and no column measures bike shelters. The idea is the author's opinion: “I believe it would move dozens of students out of cars.”

Trap Agreeing with the author, not the data

The hardest choices repeat the author's own opinion and attach a real number from the figure. Because the number is right and the opinion is the passage's, the choice feels proven.

Check what that number measures. A count of how people traveled, voted or visited can't show what they would do if something changed, or why they did what they did. If no row or column measures the exact claim, the figure doesn't support it, however strongly the author believes it.