SAT Data Analysis Practice: Percentages, Means & Samples

Know what you are practicing

Problem-Solving and Data Analysis is one of the SAT's four Math content areas. College Board's Math overview identifies it alongside Algebra, Advanced Math, and Geometry and Trigonometry. These original teaching examples are not official questions and do not reproduce a full SAT module.

Example 1: A discount followed by an increase

A jacket costs $120. Its price is reduced by 25%, then the reduced price is increased by 10%. What is the final price?

Pause and solve before reading on. The first percentage is based on $120; the second is based on the new price.

Solution: 120 × 0.75 = 90. Then 90 × 1.10 = $99. Adding −25% and +10% to get a single 15% decrease would use the wrong base for the increase.

Transfer check: Starting at $80, decrease 10% and then increase 25%. The result is 80 × 0.90 × 1.25 = $90. State the base of each percentage in words.

Example 2: The missing value in a mean

Five quiz scores are 10, 12, 15, 18 and x. Their mean is 15. Find x.

Solution: The total must be 5 × 15 = 75. The known scores total 55, so x = 20. Check: (10 + 12 + 15 + 18 + 20) ÷ 5 = 15.

Common error: averaging only the four known numbers and treating that as the mean of all five. Write the number of observations before calculating.

Transfer check: Four values have mean 9. Three values are 5, 8 and 11. The fourth is 4 × 9 − 24 = 12.

Example 3: Units reveal the operation

A vehicle travels 450 miles using 18 gallons of fuel. At the same rate, how many gallons are needed for 600 miles?

Solution: 450 ÷ 18 = 25 miles per gallon. Then 600 miles ÷ (25 miles per gallon) = 24 gallons. The units cancel correctly. Multiplying 600 by 25 would produce the wrong quantity.

Transfer check: If the rate changes, the old proportion no longer applies. Identify the assumption of a constant rate before using proportional reasoning.

Example 4: A survey with a sampling limitation

A student asks 60 members of the school chess club whether the school should offer more chess activities. Most say yes. Can the student conclude that most students in the school favor more chess activities?

Solution: No. The sample consists only of chess-club members, who may have different interests from the entire school. A larger sample from the same club would not fix that selection limitation. A sampling design covering the target population would support a better inference.

Turn errors into a practice task

If you missed Example 1, practice changing percentage bases. If you missed Example 2, write total = mean × count before solving. If Example 3 went wrong, carry units through the calculation. If Example 4 was difficult, separate the sample from the population you want to describe. Review a fresh example afterward; recognizing this explanation is not the same as applying it independently.