SAT Math problem solving and data analysis: percentages, rates and statistics

The seven skill areas and what to know for each

Skill areas are the College Board's skill/knowledge testing points for this domain (Assessment Framework for the Digital SAT Suite), checked 6 October 2026.

The key ideas

Percentages are best handled as multipliers. A 20% increase multiplies by 1.2, a 20% decrease multiplies by 0.8, and two changes in a row multiply together. That is why a 20% rise followed by a 20% fall leaves you at 0.96 of the start, 4% lower, not back where you began. Percent change is always (new - old) / old.

Unit conversions work by multiplying by fractions equal to 1, such as (1000 m / 1 km), arranged so the unwanted units cancel. Writing the units on every line is the fastest way to avoid dividing when you should multiply.

Conditional probability questions say 'given that' or 'of those who'. That phrase tells you the denominator: you only count the row or column described. In a two-way table, find the right total before you find the right cell.

For data sets, the mean is pulled toward outliers and the median is not. Standard deviation measures spread; you will not need to calculate it, but you must compare it: data bunched close to the mean has a smaller standard deviation. For studies, remember two rules: results can be extended only to the population the random sample was drawn from, and only an experiment with random assignment to treatments can show cause and effect.

Worked example 1: successive percentage changes

Question: A jacket priced at 250 is increased by 20%, then the new price is reduced by 20%. What is the final price, and what is the overall percent change?

1. Increase by 20%: multiply by 1.2. 250 × 1.2 = 300.
2. Decrease by 20%: multiply by 0.8. 300 × 0.8 = 240.
3. Overall multiplier: 1.2 × 0.8 = 0.96, so the price fell by 4%.
4. Answer: 240, a 4% decrease. Check: (240 - 250) / 250 = -10/250 = -0.04.

Worked example 2: a rate with units

Question: A car uses 6.5 litres of fuel per 100 kilometres. How many litres does it use on a 340-kilometre trip, and what does the fuel cost at 2.5 per litre?

1. Set up the rate as a fraction: 6.5 litres / 100 km.
2. Multiply by the distance so km cancels: 340 km × (6.5 litres / 100 km) = 22.1 litres.
3. Cost: 22.1 litres × 2.5 per litre = 55.25.
4. Answer: 22.1 litres, costing 55.25. Writing the units shows the km cancel, confirming you multiplied the right way.

Worked example 3: conditional probability from a two-way table

Question: A school surveyed 200 students. In grade 10, 30 joined the maths club and 70 did not. In grade 11, 45 joined and 55 did not. If a student who joined the club is chosen at random, what is the probability the student is in grade 11?

1. 'Given that the student joined' restricts you to the club column: 30 + 45 = 75 students.
2. Of those 75, the number in grade 11 is 45.
3. Probability = 45/75 = 0.6.
4. Trap: 45/200 = 0.225 is the probability that a random student is in grade 11 and joined, which answers a different question.

Worked example 4: an outlier, mean and median

Question: The numbers of books read by seven students are 4, 5, 5, 6, 7, 9 and 30. If the value 30 is removed, what happens to the mean and median?

1. With 30: the sum is 66, so the mean is 66/7 ≈ 9.43; the median (4th value) is 6.
2. Without 30: the sum is 36 across 6 values, so the mean is 6; the median is the average of 5 and 6, which is 5.5.
3. The mean fell by about 3.4, the median by only 0.5.
4. Answer: both decrease, but the mean decreases much more, because the outlier pulled it up.

Common mistakes that cost marks

• Adding successive percentages (20% up and 20% down is not zero change).
• Using the whole table total as the denominator in a 'given that' probability.
• Treating a margin of error as certainty: a sample mean of 3.2 hours with a margin of error of 0.4 means the population mean is plausibly between 2.8 and 3.6, not exactly 3.2.
• Claiming cause from an observational study, or extending a result to a wider population than the one sampled.
• Dividing instead of multiplying in unit conversions because units were not written down.
• Reading a scatterplot's axis scale wrongly, especially when an axis does not start at zero.

Exam technique and how a tutor helps

These questions are long, so read the final sentence first to know what you are looking for, then read the context. Write the calculation as a line of working before typing anything into a calculator. For tables and graphs, put your finger, or cursor, on the exact row and column the question names. On statistics claims, look for the words 'randomly selected' and 'randomly assigned': the first decides who the results apply to, the second whether cause can be claimed.

Because the domain is only 5 to 7 questions, it rarely deserves weeks on its own, but the habits it needs (careful reading, units, denominators) also protect marks in Algebra and Advanced Math context questions.

In one-to-one lessons a tutor works through mixed sets of these questions with the student, asking them to say aloud which number is the denominator or which group the study sampled before calculating. That spoken step is usually where the mistake was, and once the student hears themselves make it, it stops. Students whose first language is not English often benefit most here, because the difficulty is the reading.

Self-check: can you do these?

• A shirt costs 80 after a 20% discount. What was the original price? (Answer: 100)
• Convert 72 km per hour to metres per second. (Answer: 20 m/s)
• Find the mean and median of 2, 3, 3, 8, 9. (Answer: mean 5, median 3)
• In worked example 3, what is the probability that a grade 10 student joined the club? (Answer: 30/100 = 0.3)
• A random sample of students at one school finds a result. Can it be extended to all teenagers in the country? (Answer: no, only to students at that school)