Evidence in Tables and Graphs

Why quantitative evidence trips people up

A weather app says it rained on 40 percent of days last month. A friend says it rained on 12 days. Both can be true of the same month, and neither one alone tells you the other: you need to know the month had 30 days to connect the percentage to the count. People move between a share and a number, a level and a change, a total and a rate, constantly and usually without noticing. On the SAT, confusing those quantities becomes a direct source of error.

This lesson covers the same skill as textual Command of Evidence, in its quantitative form. A passage states a claim, and beside it sits a table, bar graph, or line graph the claim is supposed to draw on. The math stays light. The real difficulty is matching the right data relationship to the claim, because a choice that reads the numbers correctly can still answer a different question than the one the claim asks. Many quantitative errors begin with labels and units, before any arithmetic happens.

Start with the claim

Quantitative-evidence questions usually ask you to complete a data-based statement, support a conclusion, or evaluate whether the data support a conclusion. The third form asks whether the data actually bear out the claim at all, which means a choice that undercuts the conclusion can be the correct answer.

Your work has two conditions that must both hold at once. The choice has to be true of the graphic, and it has to bear on the claim. A choice that satisfies the first condition and fails the second is one of the most common ways to lose these questions. Note that on tables and graphs, a good answer is rarely the one with the biggest number; it is the one that matches what the claim is about.

Read labels and units first

Much of what decides these questions sits in the labels rather than the values. Read them in the same order every time so that the actual numbers arrive last, once you already know what they mean.

1. Title: what is being counted, and where? A choice about a different quantity fails before you check a single figure.
2. Axis or column heads: what runs across and what runs up? Time on one axis makes a trend claim possible; categories alone do not.
3. Unit: counts, percentages, rates, or amounts? A percentage and a raw number can move in opposite directions at the same time.
4. Multiplier: thousands, millions, per 100,000? A plotted 40 may stand for forty thousand cases.
5. Groups and legend: make sure you do not assign a value to the wrong series.
6. Range: where does the data start and stop? Nothing outside the plotted range can be claimed from it, however confidently a choice states it.

A graphic can also use a term the passage defines. When a column reads “recovery interval” or “effective range,” the sentence defining that exact phrase sits in the passage. Read the passage first, then the labels, then the numbers.

Check accuracy and relevance together

Ecologists tracked four ponds after removing an invasive weed and treated 30 percent native cover as recovery. They measured cover each autumn for three years.

Take the claim that native cover returned in most of the ponds within three seasons. Weigh four statements.

• “Three of the four ponds passed 30 percent by year 2 or 3 and exceeded 50 percent by year 3” is true of the data and bears directly on the claim. This is the answer.
• “Colt Mill held the highest cover in year 1” is true and says nothing about return. A starting figure carries no claim about recovery.
• “Every pond gained cover in each year” is true and bears only weakly on the claim, since Colt Mill gained every year and never came close to recovering.
• “All four ponds reached the threshold by year 3” is not even true of the data, since Colt Mill reached only 24 percent. It fails before the claim is reached.

The third statement is worth studying. Every figure behind it is accurate, and it treats a rise from 15 to 24 as though Colt Mill had recovered, when 24 still sits below the threshold the team itself set.

Keep quantities separate

These quantities are distinct, and a claim built on one cannot be carried by another, however closely related they sound.

A share alone will not hand you a count. Two districts can report the identical percentage connected and still differ tenfold in the actual number of households, because the percentages rest on different totals. Whenever a choice converts a share into a number of people or households, check first whether the graphic supplies the denominator.

Consider home internet access, as a share of all households:

Brill gained 28 percentage points and Corby gained 18. Measured against where each began, Brill grew by roughly two thirds. Both measures put Brill first here, but they can part company: a district going from 5 to 10 percent doubles its share while gaining only 5 points, and one going from 60 to 70 gains 10 points while growing by only a sixth. “Highest in 2023” is a level, and it names Ashby, the district that gained the least. “Narrowed the gap with Ashby” compares two districts at two dates, and it names Brill, whose distance behind Ashby fell from 37 points to 19.

Worked patterns

Totals versus rates

A county argues that smaller towns draw more library use per resident. A raw total of visits cannot answer a per-resident question. Ashby (60,000 residents, 240,000 visits) has 4.0 visits per resident; Brill (12,000 residents, 96,000 visits) has 8.0. The best evidence sets small towns against large towns on that exact measure. A choice that cites Ashby’s 240,000 visits is true and argues the opposite.

Endpoints and trends

A warbler’s first arrival fell from day 118 in 2019 to day 106 in 2024, though it slipped back from 115 to 117 in 2021. “Twelve days earlier than in 2019” supports an overall earlier arrival. “Earlier in every year” is false. A trend across a period does not require every interval to move the same way, but a claim of change “in each year” does. A claim about 2030 reaches beyond the table entirely.

Level versus change

A town can finish at 84 percent after rising 10 points while another finishes at 69 percent after rising 29. Highest at the end and biggest gain are different facts. If the claim is about gain, you need a starting point and an ending point for every group in the comparison.

Multipliers, groups, and the base of a percentage

If a chart reads “sales, in thousands of units” and shows 85, the company sold 85,000 units. A value can also be real and still attached to the wrong row, such as the wrong site or year. Likewise, 30 percent of 2,000 surveyed voters is 600 people, while 45 percent of 500 young voters is 225 people. The percentages can be compared as shares, but they cannot be added or turned into a head-to-head count without their separate totals.

Gaps, thresholds, and ranges

Narrowing is not catching up. A gap shrinking from 37 points to 19 closes about half the distance. It does not mean the groups are equal or that their order reversed, and it does not tell you the higher group fell; it may simply have risen more slowly.

Use only thresholds the passage defines. Water clarity rising from 40 to 55 percent has improved. It has not “recovered” unless the passage states what recovery means.

Threshold versus ranking. A cutoff question is yes or no for each group. Which group finished highest is a separate question.

Stay within the plotted range. A chart covering ages 40 to 70 says nothing about people under 40 or about age 75.

Subgroups stay subgroups. A result for women aged 65 to 74 is not a result for all older adults. An overall improvement can hide a decline in a named subgroup, so a claim about a subgroup needs that subgroup’s own data.

Read ranges as ranges. A value reported as “17 to 21” falls somewhere in that interval; you cannot conclude the mean is 19. “35 or higher” sets a floor and no ceiling. If one fiber ranges from 10 to 28 microns and another never drops below 15, the first can be finer at its low end, but you cannot say it is finer in every case.

Averages, cumulative totals, and indexes

• A mean is not every individual. An average of 6.5 hours of sleep does not mean each person slept 6.5 hours. When one extreme value is present, the median usually represents the typical case better than the mean.
• Cumulative values are not interval values. If cumulative sales were 350 by April and 600 by May, May’s own sales were 600 minus 350, or 250.
• An index is relative to a base. If the base year is 100, a reading of 115 means 15 percent above the base year, not 115 units and not a 115 percent increase.
• A non-zero axis exaggerates differences. Bars labeled 52 and 58 on an axis starting at 40 look wildly different. Read the labeled values, not the visual gap.
• A blank is not a zero. “Not reported” is missing data, not a measured zero.

Association, causation, and controls

A chart showing that regions with more parks have higher life expectancy supports an association. It does not establish that parks cause longer lives. When a program group improves 15 points and a control group improves 13, the difference in changes is only 2 points. Compare changes to changes, not endpoints to endpoints and not one group’s raw gain in isolation. Whether a difference reflects a genuine effect depends on the study design, not on the arithmetic alone.

Error bars deserve the same discipline. Standard deviation, standard error, and a confidence interval are different things. If the passage states its own rule, such as “non-overlapping intervals indicate a significant difference,” follow that rule exactly. If it states none, do not infer significance, or the lack of it, from overlap alone.

Translate the claim into a numerical pattern

Passage claims are often concepts rather than numbers. Before scanning the values, decide what shape in the numbers would demonstrate the concept.

For a wide table with several categories, filter before you compare: identify the category the claim restricts itself to, remove every row outside it, then apply the operation (earliest, highest, largest change), and finally check that the choice reattaches the right category label. The earliest reading in the whole table may be a shipboard measurement when the claim concerns buoys.

The method

1. Read the passage and find the claim the question makes you carry.
2. Read the labels: title, axes or columns, units, multiplier, groups, range.
3. Say what the data show in one sentence before opening the choices.
4. Test each choice twice: is it true of the graphic, and does it touch the claim?
5. Recheck the unit and the noun around each number. Households or share of households? Injuries or injuries per 1,000 cyclists? Final level or change? Points or percent?

Before trusting a choice, verify it in a fixed order: does the number match the graph, does the unit match, does the group match, does the year or condition match? A choice can pass the first test and fail any of the next three.

Compare close statements

Many hard choices use the same numbers; the difference lies in the sentence built around them. Know these pairs: count versus share; percentage points versus percent change; level versus change; total versus per-person rate; narrowed the gap versus caught up; overall decrease versus decreased every year; lower endpoint versus downward trend; correlation versus causation; overall sample versus subgroup; crossed the threshold versus finished highest; observed range versus beyond the range; no data versus zero. When two choices are both numerically true, return to the claim and ask which one actually carries it.