Quiz 3 — Tables and Graphs

The Guide

Reading a chart on purpose

A graph is an argument made out of ink. Somebody chose what to measure, chose what to leave out, and chose the scale. Reading one well means seeing the numbers underneath the picture, because the picture can say more than the numbers do.

Four shapes, four jobs

Line graph: Shows how one thing changes over time. Steep means fast change. Flat means little change. Downhill means decreasing, even if the line is still high up.
Bar graph: Compares separate categories side by side. The bars are not connected because there is nothing between them — no in-between value exists between Center A and Center B.
Circle graph: Shows parts of one whole. All the slices add to 100 percent. It cannot show change over time, and it cannot compare two different wholes.
Scatterplot: Shows whether two measurements move together. Each dot is one thing — one person, one plant, one day — measured twice.

Thirty seconds before you read a single value. Read the title. Read both axis labels. Read the units. Read the key, if there is one. Most wrong answers on graph questions come from confidently reading the wrong line, or reading grams as milligrams.

Where the traps live: the scale. An axis that starts at zero tells the truth about size. An axis that starts at 60 makes a difference of nine points look like a landslide. This is not always dishonest — sometimes you need to see small differences — but the picture will overstate the gap, and you should look at the numbers instead of the shape. Check the bottom of the vertical axis every time.

Between the points, and past the end. Estimating a value between two measured points is usually safe. Estimating past the end of the data is a guess, and the further out you go the shakier it gets. A plant growing 3 cm a week does not reach a hundred feet in a year.

Percent to count. A circle graph gives you shares. To turn a share into a number, multiply: 20 percent of 300 gallons is 0.20 × 300 = 60 gallons. The test asks this constantly, and the calculator is right there on the screen.

Worked Examples

Two questions, worked through

Table

Year	Share of household waste recycled
2019	18%
2020	21%
2021	27%
2022	26%
2023	32%

Example 1. Between which two years did the recycling rate fall?

Do not hunt for the smallest number. Walk down the column and subtract each year from the one before it: up 3, up 6, down 1, up 6. Only one of those is a fall.

Answer: between 2021 and 2022. A question about change is a question about the gaps, not the values.

Example 2. The town newsletter says the rate "has more than doubled since 2019." Does the table support that?

Double 18 and you get 36. The 2023 figure is 32. So the rate rose by a lot — 14 points, which is real progress worth reporting — but it did not double, and "more than doubled" is further still.

Answer: not supported. When a claim uses a word like doubled, half, or tripled, do the arithmetic. Those words are checkable, and on this test they are often checkable precisely because they are wrong.

The Quiz

Ten questions

Answer all ten, then press the button at the bottom. Nothing is timed.

Line graph — questions 1 to 3

1.About how much rain did Hillcrest receive in May?

A30 mm
B45 mm
C85 mm
D95 mm

2.In which month did Hillcrest first receive more rain than Riverton?

AMarch
BApril
CMay
DJune

3.Between which two months did Riverton's rainfall drop the most?

AJanuary and February
BMarch and April
CApril and May
DMay and June

Bar graph — questions 4 and 5

4.According to the graph, what was the passing rate at Center C?

A71%
B68%
C65%
D62%

5.A newsletter says, "Center D's passing rate is more than twice Center A's." Does the graph support that claim?

ANo. The vertical axis begins at 60 percent, so the bars exaggerate what is really a nine-point difference.
BYes. Center D's bar is more than twice as tall as Center A's.
CYes. Center D had the highest rate of the four.
DNo. The graph does not say how many students were tested at each center.

Circle graph — questions 6 and 7

6.Together, toilets and showers account for about how much of the water used?

AAbout one quarter
BAbout two thirds
CMore than three quarters
DA little less than half

7.A household uses 300 gallons of water indoors each day. About how much of that goes to showers?

AAbout 20 gallons
BAbout 60 gallons
CAbout 72 gallons
DAbout 200 gallons

Scatterplot — questions 8 and 9

8.What does the scatterplot show about hours studied and score?

AStudents who studied more hours tended to score higher.
BStudents who studied more hours tended to score lower.
CThere is no relationship between the two.
DEvery student who studied more hours scored higher than every student who studied fewer.

9.One point does not fit the pattern of the others. Which is it?

AThe student who studied 1 hour and scored 52
BThe student who studied 8 hours and scored 88
CThe student who studied 5 hours and scored 45
DThe student who studied 6 hours and scored 82

Table — question 10

Cereal	Calories	Sugar (g)	Fiber (g)	Sodium (mg)
Cereal A	110	12	1	190
Cereal B	190	9	5	210
Cereal C	150	3	6	140
Cereal D	120	14	2	105

Amounts are per one-cup serving.

10.A shopper wants the cereal with the least sugar and the most fiber per serving. Which one should she choose?

ACereal A
BCereal B
CCereal C
DCereal D

Send this line to your teacher

The line records which questions you missed and which answer you chose. That is more useful to your teacher than the score, because it shows where a question went wrong. If a question felt unclear even though you got it right, add its number with a question mark — for example 5? — before you send it.

Score ______ / 10 Missed — write the question number and the letter you chose:
______________________________________________________________

The Key

Answers, and the trap in each one

1. D — about 95 mm. Find May along the bottom, go straight up to the dashed line, then straight across to the numbers. B is Riverton's May figure. Two lines on one graph means every reading has a wrong answer sitting directly above or below the right one. Check the key before you read the value, not after.

2. B — April. In March, Riverton is still higher, 70 to 45. In April the dashed line has climbed above the solid one, 80 to 65. The lines cross somewhere between the two months, and April is the first month where Hillcrest is on top. C tempts because May is where the gap is widest and the crossing is most obvious to the eye. The question asked when it first happened, which is one month earlier and less dramatic.

3. C — between April and May. Riverton's drops are 5 mm from March to April and 20 mm from April to May, then 15 from May to June. The steepest downhill stretch of the solid line is the answer. B is where the line first turns downward, and "started falling" is not the same as "fell the most." Look at how far it fell, not where it began.

4. B — 68 percent. Read the label on the bar, or trace across from the bar's top to the axis. Nothing subtle here. This one is on the page to make sure the plain reading is solid before question 5 asks you to distrust the picture.

5. A — no, because the axis starts at 60 percent. Center D's bar is more than five times the height of Center A's, and the actual rates are 71 and 62. The bars are measuring the distance above 60, not the rates themselves. Nine points is a real difference and worth noticing. It is not double anything. D is the dangerous one, because it is a true statement and it reaches the right verdict. But it is not why the claim fails. Sample size would matter for a different question; here, the arithmetic alone settles it. Getting the right answer for the wrong reason will not survive the next question.

6. D — a little less than half. 24 plus 20 is 44 percent. Half would be 50. B counts too many slices. On a circle graph, add the numbers rather than judging by eye — two slices that each look like "about a quarter" can total anywhere from 40 to 55 percent.

7. B — about 60 gallons. Showers are 20 percent of the total. 0.20 × 300 = 60. A takes the 20 straight off the graph and forgets to multiply, which turns a share into a quantity by magic. C uses 24 percent, the toilet slice. Read which slice the question named before you touch the calculator.

8. A — students who studied more tended to score higher. The cloud of points rises from left to right. That is all a scatterplot can tell you: a tendency, not a rule. D says every, and one point is enough to sink it — the student who studied five hours and scored 45 did worse than someone who studied one hour. A single exception destroys a claim built with every, and it never destroys a claim built with tended to.

9. C — five hours, score 45. Every other point sits along a rising band. This one sits well below it, alone. A point like this is called an outlier. An outlier is not an error and not a reason to throw the data out. It is a question: what else was going on for that student? Sometimes the outlier turns out to be the most interesting thing on the page.

10. C — Cereal C. Two conditions means two passes. Least sugar: 3 grams, Cereal C. Most fiber: 6 grams, Cereal C. The same cereal wins both, which is why the question has a single answer. A has the fewest calories and D has the least sodium, and both columns are sitting right there inviting you to answer a question nobody asked. Read the question again before you read the table.

Your Score

What the number means

8 to 10	Solid. Check topic 3 on your map and go on to Quiz 4.
6 or 7	Close. Read the whole key, then take this again in a few days before you check the box.
5 or fewer	Worth real time. Charts appear on every part of the science test, and on the math test too, so this one pays twice.

Misses on 1, 4, or 10 mean the value was on the page and you read the wrong row, line, or column — slowing down for ten seconds fixes most of it. Misses on 2, 3, or 6 are about change and totals rather than single values: the question was about the gaps between numbers, not the numbers themselves. Misses on 5 or 8 are the ones to sit with, because both turn on a claim that goes further than the chart does.

The plate for this quiz

Almost every chart in this quiz was invented by one man. William Playfair, a Scottish engineer and something of a scoundrel, published the Commercial and Political Atlas in 1786. It contained dozens of line graphs showing England's trade over time — the first of their kind — and one bar chart, which he drew only because he could not get year-by-year figures for Scotland and had to compare places instead of years. He invented the circle graph in 1801, fifteen years later. Before Playfair, numbers lived in tables. After him, they had shapes.

Image to be placed at deployment. The Scotland plate is on Wikimedia Commons under a public domain mark, and full scans of the Atlas are on the Internet Archive.