Bar graphs compare separate categories by bar height; line graphs track how one quantity changes across an ordered axis, usually time. Before computing anything, read the vertical scale: note where it starts (a truncated axis that begins at 40 instead of 0 exaggerates differences), the gridline spacing, and the units. For bars, the height is the value and questions turn into differences, ratios or averages of heights. For lines, the slope carries the meaning — a steep upward segment is a fast increase, a flat segment is no change, a downward segment is a decrease — and the steepest segment, not the highest point, marks the greatest rate of change. A grouped or stacked bar chart layers two data series; make sure you are reading the right series (check the legend) and, for a stacked bar, that you subtract to isolate a single segment rather than reading the cumulative top.
✅ Solved examples
1. A line graph of revenue: Year 1 = $20M, Year 2 = $28M, Year 3 = $35M, Year 4 = $32M. Which one-year interval had the largest increase?
Year-over-year changes: +8, +7, −3. The largest increase is +8, from Year 1 to Year 2.
2. A bar graph shows visitors (in thousands): Mon 12, Tue 9, Wed 15, Thu 18, Fri 21. What was the average daily number of visitors?
3. A grouped bar chart shows, for 2022, imports = 60 and exports = 45 (in $ billion). Imports exceeded exports by what percent?
Difference = 60 − 45 = 15 on a base of exports = 45. (15/45) × 100 = 33.3%.
4. Quantitative Comparison. On a line graph, profit rises from 30 to 45 between Q1 and Q2, then from 45 to 55 between Q2 and Q3. Quantity A: the percent increase in Q1→Q2. Quantity B: the percent increase in Q2→Q3. Which is greater?
Q1→Q2: (15/30)×100 = 50%. Q2→Q3: (10/45)×100 ≈ 22.2%. So Quantity A is greater. (Note the later jump is larger in raw units but smaller in percent because the base grew.)
✏️ Practice — try these, take hints as needed
1. A line graph reads 100, 130, 150, 140 over four years. Which interval shows a decrease?
Compare each year to the previous.
Look for a drop.
150 to 140.
Year 3 to Year 4
2. Bars (in thousands): 8, 12, 10, 14, 16. Average value?
Add all five heights.
Sum = 60.
Divide by 5.
12 thousand
3. A grouped bar shows 2021 sales = 50 and 2022 sales = 65 ($ million). Percent increase?
Base is 50.
Change = 15.
(15/50) × 100.
30%
4. A line rises from 40 to 60, then 60 to 66. Which segment has the greater percent increase?
Compute each relative to its start.
20/40 vs 6/60.
50% vs 10%.
The first (40 to 60)
5. A stacked bar for one month shows a total of 90 with the "online" segment topping out at 90 above an "in-store" segment of 55. How large is the online segment?
A stacked bar’s top is the cumulative total.
Subtract the lower segment.
90 − 55.
35
📝 Topic test — 8 questions
Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.
if the answer choices are far apart, round and skip the calculator
GRE reference
🖩 Graphing Calculator
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