2022 AP Exam Administration Student Samples and Commentary

2022

Statistics

Sample Student Responses

and Scoring Commentary

Inside:

•

Free-Response Question 1

• Scoring Guidelines

••

Student Samples

••

Scoring Commentary

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AP® Statistics 2022 Scoring Guidelines

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

essenti

ally 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

iden

tify the specific components of the model solution that are used to determine the score.

Model Solution Scoring

(a)

The s

catterplot reveals a strong, positive, roughly

linear association between the mass and length of

bullfrogs. There are no points that seriously

deviate from the straight-line pattern of the points

in the plot.

Essentially correct (E) if the response provides

a description that includes at least three of

components 1-4 and component 5:

1. Direction of association (positive or

increasing)

2. Strength of a

ssociation (strong)

Form of association (linear or a

pproximately

linear)

4. Unusual features (no points with large

discrepancies from

the pattern (straight line)

exhibited by most of the points on the plot)

5. Context (association between length and mass

of bullfrogs)

artially correct (P) if the response satisfies

only one

or two components out of components

1-4 and component 5

if the response satisfies at least three out of

components 1-4 but does not satisfy

component 5.

Incorrect (I) if the response does not meet the

crit

eria for E or P.

Additional Notes:

• To satisfy component 4, it is sufficient to simply indicate that there are no unusual features.

• To satisfy component 5, it is minimally sufficient for the response to refer to the association or

rela

tionship between mass and length without explicitly mentioning bullfrogs.

• The strength of the response in part (a) may be considered if holistic scoring is needed.

AP® Statistics 2022 Scoring Guidelines

Model Solution Scoring

(b)

The value of the slope of the least-squares

regression line is 6.086. This value indicates that

the predicted mass of a bullfrog increases by

6.086 grams for each additional millimeter of

length.

Essentially correct (E) if the response satisfies

the following three components:

Identifies the value of the slope as 6.086

2. Provides an interpretation that references an

increase o

f a number of grams of mass for

each one-millimeter increase in length

3. Indicates that the slope represents a change in

a predi

ction using non-deterministic

language such as “predicted,” “estimated,”

“expected,” or “average”

Partially correct (P) if the response satisfies

only tw

o of the three components.

Incorrect (I) if the response does not meet the

crite

ria for E or P.

Additional Notes:

• The value of the slope, 6.086, may be rounded to 6.09 or 6.1, but not to 6, to satisfy the numerical

requirement in component 1.

• A response that only contains 6.086 in the interpretation satisfies component 1.

• A calculation of slope may satisfy component 1, provided that two points from the line are used in the

calculation.

• Units of measurements must be correctly specified for both mass and length to satisfy component 2.

• It is not required to refer specifically to the “least-squares regression line.”

AP® Statistics 2022 Scoring Guidelines

Model Solution Scoring

(c)

The coefficient of determination is

≈ 0.819.

This value indicates that 81.9% of the variation

in bullfrog mass can be explained by variation in

bullfrog length as described by the least-squares

line.

Essentially correct (E) if the res

ponse provides

a correct interpretation of

in context.

Partially correct (P) if the response provides a

generic inte

rpretation (no context)

if the response provides a reasonable but

incorrect in

terpretation of

in context.

Incorrect (I) if the response does not satisfy the

criteria for E

or P.

Additional Notes:

• Correct interpretations of

include the concept that part of the variation in the response (dependent or y)

variable i s explained by the linear relationship with the explanatory (independent or x) variable. The

response can take any of several equivalent forms, such as:

• The proportion of the total variability in the dependent (response) variable y that is explained by the

independent (expl

anatory) variable x.

• The proportion of variation in y that is accounted for by the linear model.

• The proportionate reduction of the total variation of the y-values that is associated with the use of the

independent vari

able x.

• The proportionate reduction in the sum of the squares of vertical deviations obtained by using the

least-squares line instead of the sample mean to predict values of y.

• Correct interpretation of

must explicitly relate to the dependent variable. Mention of the data,

predicted values, or no mention of the dependent variable are incorrect interpretations. Common incorrect

interpretations include:

• The percent (or proportion or part of the total) variability in th

e predicted y-values that is explained by

the linear relationship between y and x.

• The percent (or proportion or part of the total) variability in the data that is explained by the linear

relationshi

p between y and x.

• The percent (or proportion or part of the total) variability that is explained by the linear relationship

between y and x.

• The percent (or proportion or part of the total) variability in y that is on average explained by the

linear relationship between y and x.

• A reasonable but incorrect interpretati

on of

with context might include the following responses:

• 81.9% of the variation in mass and length can be accounted for by the least-squares reg

ression line.

• 81.9% of the variability in predicted mass is accounted for by the length.

• For context, the response variable (y) must be identified as mass, and the explanatory variable (x) must be

identified as

length.

• An interpretation of the correlation

between mass and length,

r = 0.819 = 0.905,

is not considered a

reasonable interpretation of

• The value of the percentage (81.9%) or proportion (0.819) of variation does not need to be specified, but

if an incorrect value is specified, the score is lowered by one level, from E to P or from P to I.

• The strength of the response in part (c) may be considered if holistic scoring is needed.

AP® Statistics 2022 Scoring Guidelines

Model Solution

(d)

(i) The largest residual in absolute value belongs

to the bullfrog with length 162 millimeters and

mass 356 grams.

(ii) The least-squares regression line overestimates

the mass of the bullfrog with length 162

millimeters. Plot 2 shows that the point for the

bullfrog with length 162 millimeters is below

the least-squares regression line.

Scoring

Essentially correct (E) if the response satisfies the

following two components:

1. The response to part (d-i) identifies the correct

bullfrog (length between 160 and 165 millimeters,

mass between 350 and 375 grams)

2. The response to part (d-ii) explicitly indicates

whether

the linear model overestimates or

underestimates mass for the bullfrog identified in

part (d-i) and provides a correct justification based

on a comparison of the identified observation to

the least-squares regression line

Partially correct (P) if the response satisfies only

one of the

two components.

Incorrect (I) if the response does not satisfy the

crite

ria for E or P.

Additional Notes:

• The comparison of the observation to the regression line in the response to part (d-ii) is satisfied if the response

does one of the following:

• Correctly indicates if the observation is below (above) the least-squares regression line in Plot 2.

• Notes that observed mass is smaller (larger) than the mass predicted by the least-squares regression line.

• Marks the observation selected in part (d-i) on Plot 2 with an indication of the vertical distance from the

least-squares regression line.

• Notes the correct sign of the residual.

• Numerical values are not required in the response to part (d-ii). If a n

umerical value is given for the predicted

mass, however, it must be reasonable. A numerical value for the predicted mass could be computed with the

formula given in the stem, e.g.,

−546 +

(

6.086

)(

162

)

= 439.9

grams, for a bullfrog of length 162 millimeters,

or a value can be read from the line shown in Plot 2. Any value between 425 and 450 should be considered a

reasonable value. Showing work is not required.

• The word overestimate with the calculated predicted value of mass is enough to satisfy component 2.

• If the wrong observation is identified in part (d-i), the response to part (d) may be scored P if the response to

part (d-

ii) correctly compares that observation to the least-squares regression line and states the correct

conclusion about overestimating or underestimating mass with justification.

• It is not required to refer specifically to the “least-squares regression line.”

AP® Statistics 2022 Scoring Guidelines

Scoring for Question 1

Each essentially correct (E) part counts as 1 point, and each partially correct (P) part counts as ½ point.

Score

Complete Response 4

Substantial Response 3

Developing Response 2

Minimal Response 1

If a response is between two scores (for example, 2 ½ points), use a holistic approach to decide whether to

score up or down, depending on the strength of the response and quality of the communication.

Sample 1A

1 of 2

Sample 1A

2 of 2

Sample 1B

1 of 2

Sample 1B

2 of 2

Sample 1C

1 of 2

Sample 1C

2 of 2

Statistics 2022 Scoring Commentary

Question 1

Note: Student samples are quoted verbatim and may contain spelling and grammatical errors.

Overview

The primary goals of this question were to access a student’s ability to (1) use data presented as a scatterplot to

describe a rel

ationship between two variables within the context of a study; (2) identify and interpret the slope of

a least-squares regression line; (3) interpret the coefficient of determination with respect to the proportion of

variation in values of the response variable that can be explained by variation in the values of the explanatory

variable; (4) identify the observation with the largest absolute residual using a scatterplot of the data with the

least-squares regression line inserted; and (5) determine if the least-squares regression line overestimates or

underestimates the value of the response for the identified observation and provide a justification based on a

comparison of the identified observation to the least squares regression line.

This question primarily assesses skills in skill category 2: Data Analysis, and skill category 4: Statistical

Argumentation. Skills required for responding to this question include (2.A) Describe data presented numerically

or graphically, (2.C) Calculate summary statistics, relative positions of points within a distribution, correlation,

and predicted response, and (4.B) Interpret statistical calculations and findings to assign meaning or assess a

claim.

This question covers content from Unit 2: Exploring Two-Variable Data of the course framework in the AP

Statistics Course and Exa

m Description. Refer to topics 2.4, 2.6, 2.7, and 2.8, and learning objectives DAT-1.A,

DAT-1.D, DAT-1.F, DAT-1.G, and DAT-1.H.

Sample: 1A

Score: 4

The response earned the following: Part (a) – E; Part (b) – E; Part (c) – E; Part (d) – E.

In part (a) the response includes strength, form, and unusual features, satisfying three of the first four components,

and satisfies

component 5, context. Part (a) was scored essentially correct (E).

In part (b) the response identifies the value of the slope by providing interpretation with context and includes

“expected” fo

r non-deterministic language, satisfying both components. Part (b) was scored essentially

correct (E).

In part (c) the response includes a correct interpretation of

in context. Part (c) was scored essentially

correct (E).

In part (d) the response identifies the correct bullfrog and indicates that it will be an overestimate with “negative

residual” for justification, satisfy

ing both components. Part (d) was scored essentially correct (E).

Sample: 1B

Score: 3

The response earned the following: Part (a) – E; Part (b) – E; Part (c) – I; Part (d) – E.

In part (a) the response includes direction, form, and unusual features, satisfying three of the first four

mponents, and satisfies component 5, context. The response does not satisfy component 2, strength. Part (a)

was scored essentially correct (E).

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Statistics 2022 Scoring Commentary

Question 1 (continued)

In part (b) the response identifies the value of the slope, provides an interpretation with context, and includes “on

average” for non-deterministic language. All three components are satisfied. Part (b) was scored essentially

correct (E).

In part (c) the response does not include a correct interpretation of

because it refers to the “predicted mass.”

The response contains mass but does not contain length; therefore, the context is not met. Part (c) was scored

incorrect (I).

In part (d) the response identifies the correct bullfrog and indicates that it will be an overestimate with

justification by calculating the predicted point. All thr

ee components are met. Part (d) was scored essentially

correct (E).

Sample: 1C

Score: 2

The response earned the following: Part (a) – P; Part (b) – P; Part (c) – I; Part (d) – E.

In part (a) the response includes direction and strength, satisfying components 1 and 2. The response includes

context, satisfying com

ponent 5. Part (a) was scored partially correct (P).

In part (b) the response identifies the value of the slope, satisfying component 1. The response provides a correct

interpretation with units, satisfyin

g component 2. However, the response does not include any non-deterministic

language, so it does not satisfy component 3. Part (b) was scored partially correct (P).

In part (c) the response does not include a correct interpretation of

and no context is included. Part (c) was

scored incorrect (I).

In part (d) the response identifies the correct bullfrog and indicates that it will be an overestimate with

justification as “the line is above the point.” All three com

ponents are satisfied. Part (d) was scored essentially

correct (E).

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