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.

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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

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:

Slope of the line of best fit — interpret as "y changes by m for every 1-unit change in x"
y-intercept of the line of best fit — predicted y when x = 0
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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