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SAT Problem-Solving: Statistics and Data Analysis

Mean vs. median (and the outlier effect), standard-deviation comparisons, scatterplots, two-way tables, and the correlation-vs-causation trap the SAT loves to set.

8 min TEKS PSD SAT Math

Statistics shows up 2–4 times on every Digital SAT — mean, median, standard deviation, scatterplots, and sampling. Most are quick if you remember which measure is sensitive to outliers and which isn't.

Measures of center

Three averages, three uses
  • Mean = sum / count — sensitive to outliers
  • Median = middle value (sort first!) — resistant to outliers
  • Mode = most frequent value — rarely tested directly
Data: 4, 7, 9, 9, 12, 14, 80 Mean = 135 / 7 ≈ 19.3 Median = 9 (the 4th value of 7 sorted) Mode = 9 (appears twice) The outlier 80 inflates the mean but leaves the median untouched.

When outliers matter

outlier median mean (pulled →)
An outlier on the right pulls the mean rightward but doesn't move the median.

SAT loves this pattern: "If the largest value is increased by 100, what happens to the mean and median?" Mean goes up by 100/n; median doesn't move (unless the largest value was already the middle).

Standard deviation = spread

You'll never compute standard deviation by hand on the SAT — but you must compare it across data sets.

Set A: 50, 50, 50, 50, 50 → SD = 0 (no spread) Set B: 10, 30, 50, 70, 90 → SD large (very spread) More spread = bigger standard deviation. Same mean is irrelevant.

Scatterplots and lines of best fit

A scatterplot question usually asks one of three things:

  1. Slope of the line of best fit — interpret as "y changes by m for every 1-unit change in x"
  2. y-intercept of the line of best fit — predicted y when x = 0
  3. Predict a y-value — plug an x into the line equation
Correlation vs. causation

SAT will trap you with "the data shows X causes Y." Reject any causation claim from observational data — only experiments support causal language.

Margin of error and sampling

The SAT tests sampling concepts loosely. Two rules:

  • Larger sample → smaller margin of error. Double the sample size, error shrinks.
  • Random sample = generalizable. Non-random (e.g., volunteer) samples can't generalize, no matter how large.

Basic probability

P(event) = favorable outcomes / total outcomes P(A and B, independent) = P(A) · P(B) P(A or B, mutually exclusive) = P(A) + P(B) Two-way table probability: read the cell value and divide by the row, column, or grand total — whichever matches the question's wording.
A bag has 4 red and 6 blue marbles. Draw one. P(red) = 4/10 = 2/5 P(blue) = 6/10 = 3/5 Probabilities of all outcomes must sum to 1.

Two-way table questions

A two-way table is the SAT's favorite stats prop. The trick is reading what the question is conditioning on:

  • "What percent of all students are X?" → divide cell by grand total
  • "What percent of juniors are X?" → divide cell by row (or column) total
  • "Given that a student is X, ..." → that's conditional probability, denominator is the X total

Finding a missing value from a known average

A staple SAT pattern: you're given an average and asked for a single missing value.

Five test scores have a mean of 84. Four of the scores are 78, 82, 90, 88. Find the fifth. Sum of all five = 84 · 5 = 420 Sum of known four = 78 + 82 + 90 + 88 = 338 Fifth score = 420 − 338 = 82 Convert mean to total sum first — algebra becomes one subtraction.

Common mistakes

  • Forgetting to sort before finding the median
  • Confusing standard deviation (spread) with mean (center)
  • Concluding causation from a scatterplot
  • Dividing by the wrong total on two-way tables
  • Generalizing from a non-random sample to a whole population

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