Bar Graphs & Line Graphs
1. Core Idea
- Bar graphs compare discrete categories. Height (or length) equals value.
- Line graphs show change over time. The slope of the line is the rate of change.
The distinction matters for the questions each invites: bars invite comparison ("which is largest?"), lines invite trend reading ("when did it grow fastest?").
2. Must-Know Rules
Bar graph variants:
| Type | What it shows |
|---|---|
| Simple bar | one value per category |
| Grouped (clustered) bar | several series side by side per category |
| Stacked bar | components summing to a total per category |
For a stacked bar, the value of a middle segment is the difference between its top and bottom edges — not the height of its top edge. This is the topic's most reliable trap.
Line graph reading:
| Feature | Meaning |
|---|---|
| Steep upward slope | rapid increase |
| Flat segment | no change |
| Downward slope | decrease |
| Steepest segment | greatest rate of change |
| Highest point | maximum value (not the maximum growth) |
Maximum value vs maximum increase. A line can reach its highest point in a year when it grew only slightly. "Largest increase" means the steepest segment; "largest value" means the highest point. GRE questions deliberately test both.
Multiple lines. Where two lines cross, the two quantities are equal. The vertical gap between them is their difference at that moment.
3. Worked Examples
Example 1 — Stacked bar
A stacked bar for 2024 shows Product A from 0 to 30, Product B from 30 to 70, and Product C from 70 to 100 (in thousands). What are the three product values?
- A = 30 - 0 = 30,000
- B = 70 - 30 = 40,000
- C = 100 - 70 = 30,000
Reading B as 70,000 is the trap.
Example 2 — Greatest increase vs highest value
A line graph shows values: 2020 = 40, 2021 = 55, 2022 = 60, 2023 = 95, 2024 = 100. In which year was the increase greatest, and in which year was the value highest?
Year-on-year increases: +15, +5, +35, +5.
Greatest increase: 2023 (a jump of 35).
Highest value: 2024 (100).
Different answers — exactly the point.
Example 3 — Two lines
Line P shows 120, 140, 160, 180. Line Q shows 200, 180, 160, 140 over the same four years. When are they equal, and what is the largest gap?
They are equal in year 3 (both 160).
Gaps: 80, 40, 0, 40. The largest gap is 80, in year 1.
4. GRE Traps
- Reading the top edge of a stacked segment as its value. Subtract the bottom edge.
- Non-zero axis origin. A bar chart starting at 50 exaggerates differences visually.
- Confusing "greatest value" with "greatest increase".
- Misreading which series is which in a grouped bar chart. Check the legend before every question.
- Assuming equal intervals on the horizontal axis. Occasionally the years skip.
- Interpolating between points on a line graph as if the data were continuous. The line connects measured points; intermediate values are not data.
- Ignoring the units multiplier ("in millions").
5. Speed Tricks
- Mark the legend before you start — a five-second habit that prevents series mix-ups.
- For "greatest change" questions, look for the steepest segment rather than computing every difference.
- For stacked bars, write each segment's value in the margin once and reuse it across all three questions in the set.
- Compare bar heights visually to shortlist, then compute only the finalists.
- Where lines cross, the values are equal — often the answer to "in which year were X and Y the same".
- Estimate to the nearest gridline when the question says "approximately".
6. Self-Check
Q1. A stacked bar shows segments ending at 25, 60 and 90. What is the value of the second segment?
Q2. Values across five years are 30, 45, 50, 48, 70. In which year was the percent increase largest?
Q3. A bar chart's y-axis is labelled "sales (in thousands)". A bar reaches 8.5. What is the actual value?
Answers
A1. 60 - 25 = 35.
A2. Increases: +15 (on 30 = 50%), +5 (on 45 = 11%), -2, +22 (on 48 = 46%). Largest percent increase is year 2 (50%).
A3. 8,500.
7. One-Line Summary for the Board
Stacked segments are differences, not top edges. Steepest slope = fastest change; highest point = largest value.