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Unit 1: Exploring One-Variable Data

10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we compare two or more distributions of a quantitative variable fairly and completely?

Topic 1.9 Comparing Distributions of a Quantitative Variable: compare two or more distributions of a quantitative variable by shape, center, spread, and unusual features, in context, using comparative language.
A focused answer to AP Statistics Topic 1.9, on comparing two or more distributions by shape, center, spread, and unusual features using explicit comparative language, with a worked side-by-side comparison.
9 min answer →

How do we describe the shape, center, spread, and unusual features of a quantitative distribution?

Topic 1.6 Describing the Distribution of a Quantitative Variable: describe a quantitative distribution by its shape, center, spread, and unusual features (outliers, gaps, clusters) in context.
A focused answer to AP Statistics Topic 1.6, the SOCS framework for describing a quantitative distribution by shape, outliers, center, and spread, with the vocabulary of skew, modality, and clusters, and worked descriptions.
9 min answer →

How do boxplots display the five-number summary, and how do we flag outliers formally?

Topic 1.8 Graphical Representations of Summary Statistics: construct and interpret boxplots from the five-number summary, and identify outliers using the 1.5 times IQR rule.
A focused answer to AP Statistics Topic 1.8, on building and reading boxplots from the five-number summary, the 1.5 times IQR rule for outliers, and what a boxplot does and does not reveal, with a worked construction.
9 min answer →

What can we actually learn from data, and what questions does statistical thinking let us answer?

Topic 1.1 Introducing Statistics - What Can We Learn from Data?: identify questions to be answered, based on variation in one-variable data, and recognize what a data set can and cannot tell us.
A focused answer to AP Statistics Topic 1.1, on how variation in data raises statistical questions, what kinds of question data can answer, and the limits of what a single data set reveals, with worked examples.
9 min answer →

Which graphs display a categorical variable, and how do we describe and compare them honestly?

Topic 1.4 Representing a Categorical Variable with Graphs: choose, construct, and interpret bar graphs and other displays of a single categorical variable, and describe the distribution of categories.
A focused answer to AP Statistics Topic 1.4, on displaying one categorical variable with bar graphs (frequency and relative frequency) and pie charts, reading and describing them, and the pitfalls of misleading scales, with worked examples.
8 min answer →

How do we organize categorical data into tables, and what do frequency and relative frequency tell us?

Topic 1.3 Representing a Categorical Variable with Tables: build and interpret frequency and relative frequency tables for a single categorical variable, and read proportions and percentages from them.
A focused answer to AP Statistics Topic 1.3, on building frequency and relative frequency tables for one categorical variable, converting between counts, proportions, and percentages, and interpreting them in context, with worked tables.
8 min answer →

Which graphs display a quantitative variable, and how do we choose between dotplots, stemplots, and histograms?

Topic 1.5 Representing a Quantitative Variable with Graphs: construct and interpret dotplots, stem-and-leaf plots, and histograms for a quantitative variable, and choose an appropriate display.
A focused answer to AP Statistics Topic 1.5, on displaying a quantitative variable with dotplots, stem-and-leaf plots, and histograms, choosing bin widths, and reading the displays, with a worked histogram construction.
9 min answer →

How do we measure the center and spread of a quantitative variable with numbers?

Topic 1.7 Summary Statistics for a Quantitative Variable: calculate and interpret measures of center (mean, median) and spread (range, IQR, standard deviation, variance), and judge their resistance to outliers.
A focused answer to AP Statistics Topic 1.7, defining and computing the mean, median, range, IQR, variance, and standard deviation, explaining resistance to outliers, with full worked calculations.
10 min answer →

How do we classify variables, and why does the type of variable decide everything we do next?

Topic 1.2 The Language of Variation - Variables: classify variables as categorical or quantitative, and quantitative variables as discrete or continuous, and explain why the type determines the appropriate graphs and statistics.
A focused answer to AP Statistics Topic 1.2, classifying variables as categorical or quantitative (and discrete or continuous), with the consequences for which displays and summaries are valid, plus worked classification examples.
9 min answer →

How does the normal model let us turn a value into a percentile using z-scores and the empirical rule?

Topic 1.10 The Normal Distribution: use z-scores, the empirical (68-95-99.7) rule, and the standard normal model to find proportions and percentiles for approximately normal data.
A focused answer to AP Statistics Topic 1.10, on the normal model, standardizing with z-scores, the 68-95-99.7 empirical rule, and finding proportions and percentiles, with full worked z-score and normal-area calculations.
10 min answer →