9.2 Data Interpretation: Tables, Graphs & Frequency Distributions

Data Interpretation: Tables, Graphs & Frequency Distributions

Quick Answer: GRE DI questions come in sets of 2–3 around shared data. Read the table or graph once — note scales, units, and totals — then answer each question. Graphical data IS drawn to scale, so visual estimation is fair game. The biggest traps are percent vs. percentage point, unit mismatches (thousands vs. millions), and pie charts with an implied 'Other' category.

The DI Set Format

On the GRE, DI questions appear in clusters. A single table or graph is followed by 2–3 questions, each using the same data. This is efficient: 30 seconds invested up front in understanding the data pays off across all three questions. Always:

1. Read the title and any subtitle (they define what is being measured).
2. Check the units (dollars, thousands of dollars, percent, millions of people).
3. Note whether values are exact or rounded, and whether row/column totals are given.
4. Identify the highest and lowest values — DI questions often ask about extremes.

Reading Tables

Tables organize data into rows and columns, often with marginal totals (row totals at the right, column totals at the bottom). A frequent trap: a cell value looks like a total but is actually a subtotal. Always check whether the bottom-right cell equals the sum of row totals and the sum of column totals — if it does, the table is fully specified; if not, a category is missing.

Sample Table — Enrollment by School and Year (thousands)

The bottom-right cell 1,775 equals both the sum of the right column (1,265 + 295 + 215) and the sum of the bottom row (570 + 600 + 605), confirming the table is internally consistent.

Bar Graphs and Line Graphs

Bar graphs compare discrete categories. Vertical bars show values; bar heights are drawn to scale. Line graphs show trends over a continuous variable (usually time). Multiple series can be plotted on the same axes — check the legend.

Watch for:

• Broken axes (a zigzag near the base) — magnifies differences; estimate the true gap.
• Stacked bars — segment heights add; the top of the stack is the total.
• Dual y-axes — left axis for one series, right for another; mixing them is a common trap.

Circle (Pie) Graphs

A pie chart represents parts of a whole. Each sector's angle is proportional to its share:

percent of total = sector angle / 360

If a sector labeled "Marketing" subtends 90°, Marketing is 90/360 = 25% of the total. Pie charts always sum to 100% (or 360°) — if the labeled percents sum to less than 100, an "Other" or "Unaccounted" category is implied.

Worked Example — Pie Chart with Missing Category

A company's budget pie shows: Research 35%, Marketing 25%, Operations 20%, Salaries 15%. Sum = 95%. The remaining 5% is an implied category (likely "Other" or "Profit"). A GRE question might ask "What percent is unaccounted for?" — answer: 5%.

Scatterplots

A scatterplot shows the relationship between two variables, one on each axis. Each point is one observation. Pattern reading:

• Positive association: points trend up-right.
• Negative association: points trend down-right.
• No association: scattered cloud.
• Linear vs. non-linear: straight-line pattern vs. curved.

The GRE does NOT test correlation coefficients or regression (that would be inferential statistics — out of scope). You only need to describe the visual pattern.

Frequency Distributions

A frequency distribution counts how many observations fall into each category or bin.

• Relative frequency = frequency / total (often expressed as a percent).
• Cumulative frequency = running total of frequencies up to that bin.
• Cumulative relative frequency = running total of relative frequencies; reaches 1.0 (100%) at the last bin.

Sample Frequency Distribution

Histograms vs. Bar Charts

• Histogram: contiguous bars, continuous data (score ranges, ages, incomes). Bar height = frequency. When bin widths are equal, height is proportional to frequency; when widths vary, AREA equals frequency.
• Bar chart: separated bars, categorical data (countries, months, brands). Height = value.

GRE trap: a histogram with unequal bin widths can show a taller bar over a wider bin with fewer observations — always check whether height or area encodes frequency.

Percent vs. Percentage Point — A Top DI Trap

If a rate rises from 40% to 50%:

• The percentage-point change is 50 − 40 = 10 percentage points.
• The relative (percent) change is (50 − 40)/40 × 100 = 25%.

GRE questions exploit the confusion: "The unemployment rate increased by 5%" is ambiguous, but ETS typically means 5 percentage points when discussing rates. Read carefully.

Unit Conversions

DI data often comes in thousands, millions, or billions. A table labeled "Revenue (thousands of dollars)" with value 4,500 means $4,500,000. Forgetting the unit multiplier is the most common DI arithmetic error. Always write the unit next to the number when you copy it onto scratch paper.

Sample DI Set — Two Worked Questions

Shared data: The table below shows a company's quarterly sales (in thousands of units) by region.

Question 1: In Q4, what percent of total sales did the North region account for (to the nearest whole percent)?

• Q4 total = 20 + 14 + 12 + 16 = 62.
• North share = 20/62 ≈ 0.3226 → 32%.

Question 2: From Q1 to Q4, the East region's sales increased by what percent (to the nearest whole percent)?

• Percent change = (12 − 6)/6 × 100 = 100%. East's sales doubled.

These two questions show why reading the data once pays off: the table is loaded into working memory, and each question becomes a quick calculation.