Unit 1: Exploring One-Variable Data
AP Statistics: 49 practice questions with detailed explanations.
Unit Study Guide
Executive Summary
Data comes in types; each type gets its own display and summary. Center, spread, shape, and outliers describe any distribution.
Variables and displays
Categorical variables sort into groups (bar charts, pie charts). Quantitative variables are numeric: discrete counts, continuous measurements. Histograms show distribution shape; stemplots keep every value; boxplots summarize with the five-number summary (min, Q1, median, Q3, max).
Center and spread
Mean = sum / n, pulled by outliers. Median = middle value, resistant to outliers. Range = max - min. IQR = Q3 - Q1 (middle 50%). Standard deviation measures typical distance from the mean; variance is its square. Adding a constant shifts center but not spread; multiplying scales BOTH by the factor.
Shape and outliers
Symmetric, skewed right (mean > median), skewed left (mean < median). Outliers lie beyond Q1 - 1.5·IQR or Q3 + 1.5·IQR. Use mean + standard deviation for symmetric data; median + IQR for skewed data.
The normal distribution
Bell-shaped and symmetric: mean = median = mode. The empirical rule: 68% within 1 σ, 95% within 2, 99.7% within 3. z-scores measure standard deviations from the mean: z = (x - mean) / σ.
Exam traps
Compare distributions with shape, center, spread, AND outliers. Range is not IQR. The empirical rule needs a normal shape.