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AP Statistics / Exploring One-Variable Data and Collecting Data

Lesson

Reading one-variable distributions

Choose a display, then describe shape, center, spread, and unusual values.

Learning goals

  • Match a variable type to an appropriate graph and summary.
  • Write a short description of a distribution in context.

Explanation

Start with the variable. Counts in named categories belong on a bar chart or table. Measurements on a number line belong on a histogram, boxplot, or stemplot. The display is a tool, not the answer.

A useful description names shape, a measure of center, a measure of spread, and any unusual points. Mean and standard deviation fit fairly symmetric data. Median and IQR hold up better when the tail is long or a few values sit far from the rest.

Key terms

  • Distribution. The pattern of values a variable takes, including shape, center, spread, and unusual points.
  • Standard deviation. A typical distance of values from the mean, useful when the distribution is not badly skewed.

Common mistakes

  • Reporting only the mean when the graph is clearly skewed.
  • Calling a bar chart a histogram because both use bars.

Practice

Original Marlow Works items. Check the answer explanation after you try.

1 of 1Exploring One-Variable Data and Collecting Data · easy · multiple choice

A reporter stands at one grocery-store exit and asks shoppers whether they support a new park tax. Why is this a poor way to estimate citywide support?

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Answer explanation

Commute times for 40 students are strongly right-skewed. Which pair of numbers should you lead with, and why?

Answer. Median and IQR, because they are less pulled by the long right tail.

The mean and standard deviation chase extreme late commutes and can overstate a typical trip.

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Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

  • Official / link only

    AP Statistics course page

    Official revised 2026–27 five-unit framework.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

  • CC BY — attribution required

    Collaborative Statistics

    Open statistics text for distributions, probability, and inference.

    Open Textbook Library listing · CC BY · accessed 2026-10-01

    Open source