AP Stats · Unit 1 Progress Check

AP Statistics Unit 1 Progress Check Exploring One-Variable Data walkthrough.

AP Statistics Unit 1 is one-variable data, and the Unit 1 Progress Check MCQ is about describing distributions and choosing the right summary statistic. This walkthrough covers what the questions test, the traps, and how to reason through them. Explanations only — no AP Classroom answer keys.

Updated August 2026Written by Mahmudul HasanFree · No signup

What Unit 1 covers

Unit 1 is Exploring One-Variable Data. Exploring one-variable data is 15–23% of the AP Statistics exam — the heaviest unit in the course.

Describing distributions

Shape, center, spread, and unusual features — the SOCS framework.

Graphical displays

Dotplots, histograms, stemplots, and boxplots, and when each is appropriate.

Center and spread

Mean versus median, standard deviation versus IQR, and which resists outliers.

The Normal distribution

The empirical rule and z-scores.

Outliers

The 1.5 × IQR rule for identifying them.

Comparing distributions

Describing two distributions in the same terms.

The Progress Check MCQ: what each question type tests

These are the question patterns that recur on this Progress Check, and what each one is really asking.

Choose the right summary

For a skewed distribution use median and IQR; for roughly symmetric use mean and standard deviation.

Read a boxplot

Identify the five-number summary and spot outliers using the IQR rule.

z-score reasoning

A z-score is how many standard deviations a value sits from the mean.

Empirical rule

68, 95, 99.7 percent of data within 1, 2, and 3 standard deviations of the mean for a Normal distribution.

Compare distributions

Always compare shape, center, and spread — not just one of them.

The Progress Check FRQ

Unit 1 free response usually asks you to describe or compare distributions and justify a choice of statistic. Points come from addressing shape, center, and spread with context, using resistant measures for skewed data, and comparing distributions in parallel terms rather than describing each separately.

Where students lose the most points

Using the mean for a skewed distribution

The median resists skew and outliers; the mean gets pulled toward the tail.

Describing only center

A full description covers shape, center, spread, and outliers.

Confusing standard deviation and IQR

Both measure spread, but IQR is resistant and standard deviation is not.

Applying the empirical rule to non-Normal data

It only holds for approximately Normal distributions.

Comparing distributions in different terms

Describe both using the same characteristics, side by side.

How to work through this unit

For any distribution question, run through shape, center, spread, and outliers in order, and let the shape choose your statistics — median and IQR when skewed, mean and standard deviation when symmetric.

Once you have finished the Progress Check, put your raw score into our AP Statistics Calculator to see roughly where that pace puts you on the 1–5 scale, and use the AP Statistics Review for the full exam format and study plan.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

What does the AP Statistics Unit 1 Progress Check cover?

One-variable data: describing distributions by shape, center, spread, and outliers, graphical displays, mean versus median, the Normal distribution and z-scores, and comparing distributions.

When should I use the median instead of the mean?

Use the median and IQR for skewed distributions or data with outliers, because they resist extreme values. Use the mean and standard deviation for roughly symmetric distributions.

What does the empirical rule say?

For an approximately Normal distribution, about 68% of data lies within one standard deviation of the mean, 95% within two, and 99.7% within three.

Do you post AP Statistics Unit 1 answers?

No. We publish walkthroughs of the reasoning and traps rather than AP Classroom answer keys.