The SAT Problem Solving section is packed with data displays. You'll need to extract information quickly, make calculations, and draw conclusions. Here's how to handle each type.
Bar Charts and Bar Graphs
Bar charts use rectangular bars to compare categories.
What the SAT asks:
- Which category is largest/smallest?
- What's the difference between two categories?
- What fraction/percent of the total is one category?
Example 1: A bar chart shows monthly sales: Jan = 200, Feb = 350, Mar = 300, Apr = 450.
Total sales:
Fraction in April:
Histograms
Histograms look like bar charts but display continuous data in ranges (bins).
Key difference from bar charts: There are no gaps between bars, and the x-axis shows ranges.
Example 2: A histogram shows test scores:
| Score Range | Frequency |
|---|---|
| 60-69 | 4 |
| 70-79 | 8 |
| 80-89 | 12 |
| 90-100 | 6 |
Students scoring 80 or above:
Total students:
Percent scoring 80+:
Two-Way Tables (Frequency Tables)
These organize data by two categories simultaneously.
Example 3:
| Passed | Failed | Total | |
|---|---|---|---|
| Studied | 45 | 5 | 50 |
| Didn't Study | 20 | 30 | 50 |
| Total | 65 | 35 | 100 |
"What fraction of those who studied passed?" →
"What fraction of those who passed had studied?" →
Notice the different denominators — the SAT is testing whether you pick the right total.
Line Graphs
Line graphs show change over time. Look for:
- Increasing/decreasing trends
- Steepest/flattest sections (rate of change)
- Peaks and valleys
Example 4: A line graph shows temperature rising from 60°F at 8 AM to 80°F at 2 PM.
Rate of change: per hour.
Pie Charts (Circle Graphs)
Pie charts show parts of a whole. Each slice is a percentage of the total.
Example 5: A pie chart shows a student's monthly budget of 1{,}200$: Rent 40%, Food 25%, Transport 15%, Other 20%.
Rent: 480$
Food: 300$
Reading Data Carefully
SAT data questions often include:
- Titles and labels — read them! They tell you what the numbers mean
- Units — thousands? millions? percent?
- Footnotes — extra conditions or definitions
Practice Problems
Problem 1: In the two-way table above, what percentage of all students failed?
Solution
Problem 2: A histogram shows ages of 50 employees: 20-29 (10), 30-39 (15), 40-49 (18), 50-59 (7). What fraction is under 40?
Solution
Problem 3: A pie chart shows that "Entertainment" is 12% of a 2{,}500$ budget. How much is spent on entertainment?
Solution
300$
Key Takeaways
- Read titles, axis labels, and units before answering any question
- For two-way tables, always identify the correct denominator (row total vs. column total vs. grand total)
- Histograms show ranges; bar charts show categories
- On the SAT, the math is simple — the challenge is reading the display correctly
- When in doubt, add up the relevant numbers from the table or chart
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