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.
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
Example 1
Loading…
Example 2
Loading…
Common pitfalls
Confusing mean with median
Loading…
Forgetting how scaling affects SD
Loading…
Over-generalizing study results
Loading…
Calculating mean by averaging the averages
Loading…
Key takeaways
Loading…
Loading…
Loading…
Loading…
Loading…
Tracks your progress across lessons.
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.
Mean (average): sum the values, divide by how many. Sensitive to outliers.
mean=nx1+x2+⋯+xn
Median: the middle value when sorted. With an even count, average the middle two. Resistant to outliers.
Mode: the most frequent value. Useful for categorical data.
Range: max minus min. A simple measure of spread.
Standard deviation (SD) measures how spread out the data is. SAT problems rarely ask you to compute SD — instead they ask you to compare two datasets:
"Which dataset has the larger SD?" → the one whose values are spread further from the mean.
"What happens to SD if you add the same number to every value?" → SD doesn't change (it's a measure of spread).
"What happens to SD if you multiply every value by 2?" → SD doubles (spread doubles).
Mean vs median trick. If a dataset is skewed by outliers, the mean shifts toward them but the median doesn't.
"Which is greater, the mean or the median, for the salaries: $30k, $32k, $33k, $35k, $200k?" → mean is dragged up by the $200k outlier; median is $33k. Mean > median.
Generally:
Right-skewed (long tail on the right) → mean > median
Left-skewed (long tail on the left) → mean < median
Symmetric → mean ≈ median
Sampling and inference. When the SAT shows a study and asks if conclusions can be generalized:
Random sample from the target population → conclusions about the population are valid.
Random assignment to treatment/control → conclusions about causation are valid.
Both → can claim cause-and-effect about the population.
Neither → can only describe the sample, not generalize.
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?
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.
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.