31. Graphics interpretation
Read axes and units first. Estimate before computing.
Core ideas
- Read the axes, units, and scale FIRST. "Thousands of units" versus "units" is where wrong answers live.
- Estimate before computing. If a bar looks like it doubles, the answer near 100% growth is probably right; exact arithmetic just confirms.
- Check whether the graph shows totals, per-period values, or cumulative values before comparing points.
Worked example 1
A line graph titled "Norvane Bikes: Quarterly Shipments" has a y-axis labeled "shipments (thousands)" from 0 to 50 and an x-axis of quarters Q1 to Q4. The line passes through Q1 = 20, Q2 = 25, Q3 = 40, Q4 = 30.
Fill in: Shipments in Q3 were ___ percent greater than in Q1, and total shipments for the year were ___ thousand.
Show solution
Units first: every value is in thousands, so Q3 means 40,000 bikes, not 40. Estimate: Q3 at 40 versus Q1 at 20 looks like a doubling, so expect 100%. Compute: (40 - 20)/20 = 1 = 100 percent greater. Total: 20 + 25 + 40 + 30 = 115 thousand. Answers: 100 and 115.
Worked example 2
A bar chart titled "Pellwater Cafe: Cumulative Members" shows cumulative membership at each month's end: Jan 300, Feb 450, Mar 700, Apr 800.
Fill in: The month with the largest number of NEW members was ___, and the number of new members that month was ___.
Show solution
The trap is the word cumulative: bars show running totals, so new members each month is the difference between consecutive bars. Jan gained 300, Feb gained 450 - 300 = 150, Mar gained 700 - 450 = 250, Apr gained 800 - 700 = 100. The largest single-month gain after the starting month is Jan's 300; if the question restricts to gains, Jan with 300 wins. Answers: January and 300.
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