Statistics
SAT statistics questions are mostly about *interpretation* — knowing what mean, median, range, and standard deviation tell you, and which one a particular question is really asking for.
| Statistic | How to compute | Sensitive to outliers? | Use when |
|---|---|---|---|
| Mean | Sum / count | Yes (heavily) | Data is roughly symmetric |
| Median | Middle value when sorted | No | Data has outliers or is skewed |
| Mode | Most frequent value | No | Data is categorical |
| Range | Max − min | Yes (uses extremes) | Quick rough spread |
| Shape | Visual | Relationship |
|---|---|---|
| Symmetric | Bell-shaped | Mean ≈ median ≈ mode |
| Right-skewed | Long tail to the right (high outliers) | Mean > median (mean pulled toward tail) |
| Left-skewed | Long tail to the left (low outliers) | Mean < median (mean pulled toward tail) |
Read the question carefully — is it asking about mean, median, SD, or generalizability? Each demands a different approach.
The test scores for five students are 72, 85, 85, 90, 98. What is the mode of the scores?
Worked examples
A teacher records test scores: 72, 75, 78, 80, 82, 85, 92.
Which is greater: the mean or the median?
A researcher randomly selects 200 students from a single high school's biology class to test a new study technique. Half use the technique; half don't. The technique group scores significantly higher.
Which conclusion is most appropriate?
Common pitfalls
Mean is the average (sum / count). Median is the middle value. They're often different — especially when outliers exist. Read the question carefully.
Adding a constant to every value DOESN'T change SD (it shifts the dataset, not its spread). Multiplying every value by a constant DOES scale SD by that factor. Mixing these up costs easy points.
If a study sampled from one school, conclusions only apply to that school. Don't extend findings to populations not represented in the sample. The SAT puts trap answers that generalize too broadly.
If group A averages 80 and group B averages 70, the combined mean is NOT 75 unless the groups are the same size. Total = (sum of A) + (sum of B); combined mean = total / total count.
Key takeaways
Mean = sum / count. Median = middle value when sorted. Mode = most frequent. Range = max − min.
Outliers move the mean but not the median. Skewed-right → mean > median; skewed-left → mean < median.
Adding a constant to every value doesn't change SD. Multiplying scales SD by that factor.
Random sampling → can generalize. Random assignment → can claim causation. Need both for cause-and-effect across a population.
When two datasets are compared, larger SD = more spread out, not necessarily a larger mean.
Checkpoint
10 questions on One-Variable Data: Distributions and Measures of Center and Spread, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.