Quizzes, exams, and flashcards about Problem-Solving and Data Analysis: Data 1 — percentages, spread and what a sample proves.
← SAT
Ratios and rates, percentages, one- and two-variable data, probability, and what a sample does and does not license you to conclude — ≈15% of the Math section, 5 to 7 questions.
Six skill points, and the arithmetic in them is easy. The difficulty is almost entirely in reading:
Mean and median move differently. An outlier drags the mean towards it and leaves the median nearly alone. Any question that adds one very large or very small value to a data set is asking about that, and the answer is usually "the mean increases and the median stays the same or changes slightly".
Standard deviation is spread, not size. Two data sets with the same mean can have very different standard deviations, and a set whose values are bunched together has the smaller one. You are never asked to compute it — only to compare two sets by eye.
Only a randomised experiment supports a causal claim. This is the single most tested idea in the statistics part of the SAT, and it appears in two halves:
A wrong answer will almost always overreach in one of those two directions: a causal claim from an observational study, or a generalisation to "all adults" from a sample of volunteers at one gym.
A margin of error describes the range in which the true population value plausibly lies, and it shrinks as the sample gets larger. It says nothing about individuals and nothing about a different population. "The plausible range is 22% to 28%" does not mean any particular person is 25%.
A quantity that rises 20% and then falls 20% does not return to where it started — it ends at 96% of it. And a change from 20% to 25% is a rise of five percentage points and of twenty-five percent; questions choose their words carefully and the choices include both numbers.
