Data Interpretation

What This Module Covers

This module covers how to read and extract information from bar graphs, line graphs, pie charts, tables, and scatterplots. You'll learn the key calculations GRE Data Interpretation (DI) sets demand — percent change, percent of total, and ratios — and how to apply them quickly under time pressure. You'll also learn the traps that cause test-takers to pick a wrong answer even when they read the graph correctly.

Why It Matters on the GRE

DI questions appear in sets at the end of every Quant section, and you get 6–8 of them per test. That's a significant chunk of your score. The good news is that DI questions don't test advanced math — they test your ability to read carefully and calculate accurately. Most mistakes on DI come from misreading the graph, not from failing a hard concept. Master the fundamentals here and DI becomes one of the most reliable scoring opportunities on the test.

Core Concepts

DI Set Format

Data Interpretation questions always come in groups of three. A single graph, table, or chart is shown, and three questions — which may be Problem Solving, Quantitative Comparison, or Numeric Entry — all refer to that same visual. Because these sets appear at the end of the section, you may be tired when you reach them. Budget roughly 6–7 minutes per DI set: about 1–2 minutes to read the visual carefully, then 2 minutes per question.

Must Know: Always read the title, axis labels, units, and any footnotes before answering a single question. Missing a unit (thousands vs. millions) will cost you.

Reading Bar Graphs

Start by identifying exactly what each axis measures and what units are in use. For grouped bar graphs, note which bar belongs to which category — the legend is your guide. For stacked bar graphs, each segment's length represents a sub-quantity; to find the value of a single segment, subtract the lower boundary from the upper boundary.

Must Know: Check whether the y-axis starts at 0. If it starts at, say, 80, a bar that appears twice as tall as another may represent only a small absolute difference. The GRE exploits this visual distortion constantly.

Example — Reading a stacked bar graph:

1. Note that the y-axis shows "Revenue ($ millions)" and runs from 0 to 100.
2. Product A's bar reaches 60; Product B's segment within that bar starts at 30 and ends at 60, so Product B = 30.
3. Do NOT read Product B's height as 60 — that's the top of the whole bar, not the segment.

Reading Line Graphs

Each point on a line graph represents a value at a specific x-axis position, typically a point in time. The slope of the line between two points tells you the rate of change — steeper means faster change, flat means no change. Never assume a smooth trend continues beyond the last data point, and don't interpolate between points unless the question explicitly asks you to estimate.

Must Know: A line going up means the quantity is increasing; a line going down means it's decreasing. The steepness tells you how fast — not what the absolute value is.

Pie Charts

Every pie chart represents one whole (100%), divided into slices. To convert a slice's percentage into an absolute value, multiply: percentage × total. To find what percentage one slice is of another, divide the part by the whole and multiply by 100.

Must Know: You cannot compare absolute values between two different pie charts unless you know each chart's total. A 30% slice in Chart A could represent more units than a 60% slice in Chart B if Chart A's total is much larger.

Example — Pie chart to absolute value:

1. Chart shows "Country X's Energy Mix"; the natural gas slice = 40%.
2. A footnote states total energy production = 250 billion kWh.
3. Natural gas absolute value = 0.40 × 250 = 100 billion kWh.
4. Do not just report "40%" — the question almost certainly asks for an absolute amount.

Tables and Two-Way Tables

Read row headers and column headers before you look at any number. In a two-way table, each cell value belongs simultaneously to its row category AND its column category — this sounds obvious, but under pressure it's easy to read the wrong row. Always confirm whether a table shows raw counts or percentages; mixing up the two is one of the most common DI errors.

Must Know: When a table shows percentages, you need the row or column total to find an absolute number. When it shows absolutes, you need the total to find a percentage. Identify which you have before calculating.

Scatterplots

Each dot in a scatterplot represents one data item with a specific (x, y) value. A trend line, or line of best fit, shows the general direction of the relationship. Positive correlation means as x increases, y tends to increase. Negative correlation means the opposite.

Must Know: Correlation does NOT imply causation. The GRE will never ask you to conclude that one variable causes another — and if a trap answer implies causation, eliminate it.

Key DI Calculations

Three formulas cover almost every DI calculation you'll encounter:

• Percent change: (new − old) / old × 100%
• Percent of total: (part / total) × 100%
• Ratio: larger value / smaller value (or as directed)

Estimation is your best friend. When answer choices are spread far apart (e.g., 20%, 40%, 60%), you can often round aggressively and still identify the correct answer. Don't spend time on precise arithmetic when a ballpark gets you there.

Must Know: Each percent change is calculated on a different base. A 10% increase followed by a 10% decrease does NOT return you to the original value — you end up at 99% of the start. Never add or subtract percent changes across years as if they were absolute quantities.

Common Traps

• Y-axis doesn't start at 0: A bar chart may make a 5% difference look like a 50% difference because the axis starts at 95. Always check the scale before drawing conclusions about relative size.
• Confusing percent and absolute value: The largest slice in a pie chart is the largest by percentage, not necessarily by absolute count. Without the total, you cannot determine absolute values.
• Comparing two different pie charts without totals: You cannot say "Country A has more cars than Country B" just because Country A's car slice is larger. If Country B's total fleet is ten times bigger, its smaller slice could represent more cars.
• Adding percent changes across years: If sales rose 20% in Year 1 and 15% in Year 2, the total increase over two years is NOT 35%. Each year's percentage applies to a different base.
• Misreading grouped vs. stacked bars: In a grouped bar chart, bars sit side by side; in a stacked bar chart, they sit on top of each other. Treating one type as the other produces completely wrong readings.
• Ignoring units: A table might show values in thousands in one column and millions in another. The GRE buries unit switches in column headers — always re-read them.

GRE Strategy

• Read the full visual before touching any question. One minute of careful orientation saves three minutes of re-reading mid-question.
• Write down the total when it's given — pie chart and table questions almost always require it.
• For percent change questions, always identify which value is "old" and which is "new" before dividing.
• When answer choices are far apart, estimate aggressively. Round to the nearest 5 or 10 to simplify arithmetic.
• On Numeric Entry DI questions, double-check your units — the answer box may expect thousands, millions, or a plain integer.
• If a question feels like it requires a complicated multi-step calculation, re-read it. GRE DI questions are designed to be solvable in under 2 minutes — you're probably missing a shortcut.

Worked Example

Question: The table below shows quarterly sales (in millions of dollars) for two products over four quarters.

What was the percent increase in Product A's sales from Q1 to Q4?

(A) 25% (B) 30% (C) 33% (D) 40% (E) 56%

Solution:

Step 1 — Identify old and new values. Old = Q1 = $40M. New = Q4 = $52M.

Step 2 — Apply the percent change formula. Percent change = (new − old) / old × 100% = (52 − 40) / 40 × 100% = 12 / 40 × 100% = 0.30 × 100% = 30%

Step 3 — Select the answer. The correct answer is (B) 30%.

Step 4 — Verify. Check: $40M × 1.30 = $52M. Confirmed.

Why the other choices are wrong:

• (A) 25% — This comes from dividing 10/40 instead of 12/40. A careless misread of the Q4 value as $50M produces this error.
• (C) 33% — This is the trap for test-takers who flip the formula and calculate 12/36 or accidentally use Q4 as the denominator: 12/52 ≈ 23%... actually 33% comes from treating the change (12) over a wrong base. Any time you see ~33%, suspect a base error.
• (D) 40% — This might result from calculating (52 − 40)/30, accidentally using Product B's Q1 value as the denominator.
• (E) 56% — This is what you get if you calculate Product B's total sales relative to Product A, or confuse percent change with percent of total: 52/40 − 1 is actually 30%, but if someone multiplies instead of subtracts, they might land near here.

The key discipline: always lock in your "old" value as the denominator before doing any arithmetic. On DI, the most common error isn't a hard calculation — it's a sloppy setup.