Subtopics

Ratios, rates, and proportional reasoning

Setting up proportions, unit conversion, scale models, and working with rates in context.

Percentages

Percent increase/decrease, percent of a total, finding the original value, and multi-step percentage problems.

Probability

Basic probability, conditional probability, and probability from two-way tables.

Statistical concepts

Mean, median, mode, range, and standard deviation. Choosing appropriate measures of center and spread.

Data interpretation

Reading scatterplots, histograms, bar charts, and two-way frequency tables. Identifying trends and making inferences.

Key formulas

mean = Σx / n

P(A) = favorable / total (probability)

part / whole × 100 (percentage)

New = Original × (1 ± r/100) (percent change)

A = P(1 + r/n)^(nt) (compound interest)

See full formula sheet →

Test-taking tips

For two-way tables, re-read the question to confirm whether you need a row rate, column rate, or total rate.
Median is more useful than mean when outliers are present; the SAT tests whether you know when to use which.
Percent of percent problems: convert each percent to a decimal and multiply.
For scatterplots, line of best fit questions often just ask you to read a y-value at a given x.

Fully worked Data & Statistics example

Worked example: Reading conditional percentages from a two-way table

A school compared the results of students taking two versions of a review course.

Course format	Passed	Did not pass	Total
Online	72	48	120
In person	63	27	90
Total	135	75	210

Question: By how many percentage points does the pass rate for the in-person course exceed the pass rate for the online course?

The question compares two pass rates, so calculate the percentage within each course format.

For the online course, 72 of the 120 online students passed:

72 / 120 = 0.60 = 60%

For the in-person course, 63 of the 90 in-person students passed:

63 / 90 = 0.70 = 70%

Find the difference between the two rates:

70% − 60% = 10 percentage points

The in-person pass rate exceeds the online pass rate by 10 percentage points.

Verification method: Apply the online rate to the 90 in-person students. If that group had the same 60% pass rate, 0.60(90) = 54 students would have passed. In fact, 63 passed, which is 9 more. Since 9 / 90 = 0.10 = 10%, this confirms a 10-percentage-point difference.

Trap 1: Using the wrong denominator. The in-person pass rate is 63/90, not 63/135 and not 63/210. The phrase “for the in-person course” restricts the denominator to all students who took that version.

Trap 2: Reporting percent change instead of percentage-point change. The relative percent increase from 60% to 70% is (70 − 60) / 60 × 100% ≈ 16.7%. That is a valid calculation, but it answers a different question. The direct difference between the rates is 10 percentage points.

Why students get Data & Statistics questions wrong

Assuming the mean and median respond to an outlier in the same way.

Consider the data set 6, 7, 7, 8, 9. Its mean is 7.4 and its median is 7. If 9 is replaced by 49, the mean rises to 15.4, but the median remains 7. The mean uses the numerical value of every observation, so one extreme value can move it sharply. The median depends on the middle position and may not move at all.

Using the grand total when a question asks for a conditional rate.

In the table above, “What percentage of online students passed?” requires 72/120. Using 72/210 answers “What percentage of all students were online students who passed?” The numerator may be identical, but changing the denominator changes the population being measured and therefore changes the meaning of the result.

Turning an observed association into a causal conclusion.

If students who attended more review sessions earned higher scores, the data show an association. They do not prove that attendance caused the higher scores. Students who attended more sessions may also have studied more independently or started with stronger skills. A causal conclusion requires a study design that controls competing explanations, typically through random assignment.

Confusing percentage-point change with percent change.

An approval rate rising from 40% to 50% increases by 10 percentage points. Relative to the original 40%, however, the percent increase is (50 − 40) / 40 × 100% = 25%. Reporting 10% confuses the difference between two percentages with the change relative to the starting percentage.

Final Data & Statistics check

Before accepting a rate or probability, complete this sentence using the actual data: “I divided ___ members of the requested group by ___ total members of that same group.” If the denominator does not match the population named after words such as “among,” “given,” or “of,” the calculation answers the wrong conditional question. Then label the result explicitly as a percent, percentage-point difference, count, or probability.

Data & Statistics.