SAT Math Data and Statistics

Mean, median, IQR, standard deviation — everything you need

Statistics on the SAT isn't complicated, but it rewards careful reading. Expect 3–5 questions per section, mostly about mean, median, and interpreting data sets. The arithmetic is simple — sums and divisions — but the SAT loves traps, like adding a new value and asking for the new mean.

Core principle: mean is sensitive to outliers, median is robust. When you see a set with one very large or very small value, the median usually describes the "typical" element better than the mean. The SAT tests this intuition with "which measure best describes the set?" questions.

What the SAT actually tests

Computing the mean: sum divided by count
Finding the median (even count: average of two middle values)
Effect of adding or removing a value on the mean
Interpreting standard deviation (smaller = more clustered)
Interquartile range (IQR) = Q3 − Q1
Comparing two sets: which has higher mean, larger spread, etc.

Key concepts

Mean

Sum of values divided by count: $\overset{x}{ˉ} = \frac{\sum x _{i}}{n}$ . Sensitive to outliers.

Median

Middle value of a sorted set. For an even count, the average of the two middles. Robust to outliers.

Standard deviation

Measures spread. The SAT doesn't ask you to compute it — just to compare. A set with values spread further from the mean has higher SD.

IQR

Q3 − Q1. Measures the spread of the middle 50% of the data. Like the median, robust to outliers.

Worked examples

Example 1

The mean of 5 numbers is 12. After adding a 6th number, the mean rose to 14. What was the added number?

Solution

Sum of first 5: $5 \cdot 12 = 60$ . Sum after adding: $6 \cdot 14 = 84$ . Added number: $84 - 60 = 24$ .

💡 Mean × count = sum. The core trick for "effect of adding" problems.

Example 2

Set A: ${5, 6, 7, 8, 9}$ . Set B: ${1, 4, 7, 10, 13}$ . Which has the larger standard deviation?

Solution

Both have the same mean (7), but set B is more spread out. Set B has the larger SD.

💡 Don't compute SD — just eyeball the spread around the mean.

Common pitfalls

Computing median without sorting first. Always sort.
Confusing mean and median for outlier problems. Adding a large value moves the mean faster than the median.
With an even count — taking one middle value instead of averaging the two.
"New mean" problems — forgetting that the count changed.

Exam strategy

For mean problems, go through the sum: "mean × n = sum." For new-mean problems, compute the new sum and divide by the new count. For median — sort the set, even if it looks ordered already. For SD comparisons, never compute — just compare how far values sit from the mean. If a question asks which measure "best describes" a set with an outlier, the answer is the median.

Frequently asked questions

Mean vs median — what's the difference?

Mean = sum / count. Median = middle value after sorting. Mean is sensitive to outliers, median isn't. When a set has an outlier, the median better "describes" it.

What is standard deviation?

A measure of spread around the mean. Larger SD = more spread out. The SAT almost never asks you to compute it — just to compare the spread of two sets visually.

What is margin of error?

Range of uncertainty in a poll result. "64% ± 3%" means the true value sits between 61% and 67% at a stated confidence (usually 95%). Bigger sample = smaller margin.

Correlation vs causation?

Correlation means two variables change together. Causation means one causes the other. The SAT often tests the distinction — correlation alone does NOT prove A causes B.

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