AP® Statistics - Free-Response Question 1 Scoring Guidelines and Student Samples

Sep 30, 2026

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AP® Statistics sample student responses and scoring commentary for Free-Response Question 1, including detailed 4-point scoring guidelines. The material explains how each letter part (a–c) is evaluated using criteria for essentially correct, partially correct, and incorrect responses. Model solutions are provided alongside scoring rubrics covering distribution shape, center, spread, and unusual features, plus boxplot construction requirements. Additional notes clarify numeric bounds, acceptable approximation language, and common pitfalls.

LanguageEnglish

CategoryExam

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

General Scoring Notes

(a) Model solution and scoring criteria

Additional notes for part (a)

(b) Model solution and scoring criteria

Additional placement requirements for part (b)

2023 AP® Statistics Sample Student Responsesand Scoring Commentary Inside: Free-Response Question 1 5 Scoring Guidelines 5 Student Samples 5 Scoring Commentary © 2023 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board. Visit College Board on the web: [collegeboard.org](collegeboard.org). [AP Central is the official online home for the AP Program: apcentral.collegeboard.org](AP Central is the official online home for the AP Program: apcentral.collegeboard.org). | Question 1: Focus on Exploring Data 4 points | | | | --- | --- | --- | | | | | | General Scoring Notes
• Each part of the question (indicated by a letter) is initially scored by determining if it meets the criteria for essentially correct (E), partially correct (P), or incorrect (I) . The response is then categorized based on the scores assigned to each letter part and awarded an integer score between 0 and 4 (see the table at the end of the question) .
• The model solution represents an ideal response to each part of the question, and the scoring criteria identify the specific components of the model solution that are used to determine the score. | | | | | | | | | Model Solution | Scoring | | (a) | The histogram of dissolved oxygen concentration in Alaskan streams with water temperatures colder than 8oC is unimodal and skewed left with a median between 11 and 12 mg/l .
The first quartile is in the bin from 10-11 mg/land the third quartile is in the bin from 12-13 mg/l , so the IQR is approximately 2 mg/l .
There do not appear to be any high outliers, but there are several potential low outliers because the values in the 2-3, 4-5, and 5-6 bins are all certainly more than 1.5 IQR below the first quartile. | Essentially correct (E) if the description of the distribution satisfies component 1 AND at least three of components 2-5:
1. Includes context of dissolved oxygen concentration
2. Shape: The distribution is skewed left
3. Center: The center of the distribution is between 11 mg/l and 12 mg/l
4. Spread: Refers to at least one measure of variation (i.e., the range is between
14 – 2 = 12 mg/l and 13 – 3 = 10 mg/l; all values are between 2 mg/l and 14 mg/l or the IQR is approximately 2 mg/l)
5. Unusual features: potential outliers or a gap between 3 mg/l and 4 mg/l
Partially correct (P) if the response satisfies component 1 and two components out of components 2-5
OR
if the response satisfies at least three out of components 2-5 but does not satisfy component 1.
Incorrect (I) if the response does not meet the criteria for E or P. | | Additional Notes:
• Context
o Component 1 can be satisfied with a reference to dissolved oxygen concentration, dissolved oxygen, amount of oxygen, or mg/l. | | | • Shape: o Component 2 cannot be satisfied if a response describes the histogram as normal or approximately normal. • Center: o A response that addresses center using definitive language such as “the mean (median) of the distribution is 11.5” cannot satisfy component 3. o A response that addresses center using approximate language such as “the median of the distribution is approximately 11.5” must, for any single measure of center, specify a numeric value that is between 11 mg/l and 12 mg/l , inclusive, to satisfy component 3. • Spread: o A response recognizing all values in the sample fall between 2 mg/l and 14 mg/l , satisfies component 4 only for these exact endpoints and need not appeal to a specific measure of spread such as the range. o A response that uses interval language must use it correctly. For example,“the observations range from 2 mg/l and 14 mg/l ,” satisfies component 4 because it correctly indicates that all observations are between 2 mg/l and 14 mg/l , inclusive. However, a statement such as “the range is between 2 mg/l and 14 mg/l ,” is incorrect because the range is a single number, i.e.,

FAQs

How are letter parts scored in Free-Response Question 1?

Each letter part is first judged as essentially correct (E), partially correct (P), or incorrect (I). Then the response is categorized to award an integer score between 0 and 4 based on the combination of letter-part scores.

What distribution features must part (a) include to be essentially correct?

To be essentially correct, the response must include dissolved oxygen context and satisfy the distribution criteria: left-skewed shape, center between 11 and 12 mg/l, spread described with acceptable variation measures, and at least one appropriate unusual-feature indicator such as potential outliers or a gap.

What boxplot components are required for part (b) to be essentially correct?

Essentially correct requires all five components: box starting at Q1, box ending at Q3, median located within the box, whiskers extended to the minimum, and whiskers extended to the maximum. Partially correct includes only three of the five components.

Sep 30, 2026

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