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Grade 11 - Claim 1 - Target P

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Mathematics

Target P

Summarize, represent, and interpret data on a single count or measurement variable

Sample Item

Grade 11

Test

Claim 1

Concepts and Procedures

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Grade

Grade 11

Content Domain

Statistics and Probability

Standards

ID-1ID-2ID-3
Supporting

Standards

  • ID-1

    Represent data with plots on the real number line (dot plots, histograms, and box plots).

  • ID-2

    Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

  • ID-3

    Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Clarifications

Tasks for this target will require students to use appropriate statistics to explain difference in shape, center, and spread of two or more different data sets, including the effect of outliers.

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student will be able to represent data on the real number line with a dot plot, histogram, or box plot.

  • 2

    The student will be able to use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different...

  • 3

    The student will be able to interpret the differences in shape, center, and spread in the context of the data sets.

  • 4

    The student will be able to interpret the effects of outliers on the shape, center, and spread of a data set.

Item Guidelines

Depth of Knowledge

  • M-DOK2

    Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...

Allowable Item Types

  • Multiple Choice, single correct response
  • Hot Spot
  • Matching Tables

Allowable Stimulus Materials

data sets (listed, described contextually, or as a table of values), graphs

Key/Construct Relevant Vocabulary

mean, median, interquartile range, outlier, standard deviation

Allowable Tools

Calculator (varies by task model)

Target-Specific Attributes

None

Accessibility

Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...

Development Notes

Much of standard S-ID.A.3 will be assessed at the Claim 4 level.

Task Models

Task Model 1a

  • Item Types

    Multiple Choice, single correct response

  • Depth of Knowledge

    M-DOK2

  • Standards

    ID-1

Target Evidence Statement

  • The student will be able to represent data on the real number line with a dot plot, histogram, or box plot.

  • Allowable Tools

    None

Task Description

Prompt Features: The student is prompted to identify the plot of a given data set. Stimulus Guidelines: Item difficulty can be adjusted via these example methods, but is not limited to these methods: Presence of repeated...

Stimulus

The student is presented with a contextual data set.

Example 1

Example Stem 1: Select the dot plot that represents the given test scores.

90, 45, 85, 70, 85, 50, 75, 85, 65, 75, 60, 85, 80, 65, 80

A.
The number line is labeled Test Scores and ranges from 45 to 90. Dots are plotted: 45, 1 dot; 50, 1 dot; 60, 1 dot; 65, 2 dots; 70, 1 dot; 75, 2 dots; 80, 2 dots; 85, 4 dots; 90, 1 dot.

B.
The number line is labeled Test Scores and ranges from 45 to 90. Dots are plotted: 45, 1 dot; 50, 1 dot; 55, 2 dots; 60, 1 dot; 65, 1 dots; 70, 1 dot; 75, 2 dots; 80, 1 dots; 85, 3 dots; 90, 1 dot.

C.
The number line is labeled Test Scores and ranges from 45 to 90. Dots are plotted: 45, 1 dot; 50, 1 dot; 55, 1 dot; 60, 1 dot; 65, 2 dots; 70, 1 dot; 75, 2 dots; 80, 2 dots; 85, 4 dots; 90, 1 dot.

D.
The number line is labeled Test Scores and ranges from 45 to 90. Dots are plotted: 45, 1 dot; 50, 1 dot; 60, 1 dot; 65, 1 dot; 70, 1 dot; 75, 1 dot; 80, 1 dot; 85, 1 dot; 90, 1 dot.

Rubric: (1 point) The student selects the correct option (e.g., A).

Example 2

Example Stem 2: Select the histogram that represents the given test scores.

91, 48, 86, 73, 86, 49, 77, 86, 64, 78, 64, 82, 68, 82, 68, 82

A.
Histogram of Test Scores is shown. The horizontal axis is labeled Test Scores and ranges from 45 to 95. The vertical axis is labeled frequency and ranges from 0 to 8. 45 to 50, 2 scores. 60 to 65, 2 scores. 65 to 70, 2 scores. 70 to 75, 1 score. 75 to 80, 2 scores. 80 to 85, 3 scores. 85 to 90, 3 scores. 90 to 95, 1 score.

B.
Histogram of Test Scores is shown. The horizontal axis is labeled Test Scores and ranges from 45 to 95. The vertical axis is labeled frequency and ranges from 0 to 8. 45 to 50, 2 scores. 50 to 55, 1 score. 55 to 60, 1 score. 60 to 65, 2 scores. 65 to 70, 2 scores. 70 to 75, 1 score. 75 to 80, 2 scores. 80 to 85, 3 scores. 85 to 90, 3 scores. 90 to 95, 1 score.

C.
Histogram of Test Scores is shown. The horizontal axis is labeled Test Scores and ranges from 45 to 95. The vertical axis is labeled frequency and ranges from 0 to 8. 45 to 50, 1 score. 50 to 55, 1 score. 55 to 60, 1 score. 60 to 65, 1 score. 65 to 70, 1 score. 70 to 75, 1 score. 75 to 80, 1 score. 80 to 85, 1 score. 85 to 90, 1 score. 90 to 95, 1 score.

D.
Histogram of Test Scores is shown. The horizontal axis is labeled Test Scores and ranges from 45 to 95. The vertical axis is labeled frequency and ranges from 0 to 8. 45 to 50, 2 scores. 60 to 65, 2 scores. 65 to 70, 2 scores. 70 to 75, 2 scores. 75 to 80, 2 scores. 80 to 85, 3 scores. 85 to 90, 3 scores. 90 to 95, 1 score.

Rubric: (1 point) The student selects the correct option (e.g., A).

Example 3

Example Stem 3: Select the box plot that represents the given test scores.

48, 50, 64, 64, 68, 68, 73, 77, 78, 82, 82, 82, 86, 86, 86, 91

A.
The title of the box and whisker plot is Test Scores. The number line ranges from 45 to 95. The whiskers range from between 45 and 50 to between 90 and 95. The box ranges from 65 to 85 with a median between 75 and 80.

B.
The title of the box and whisker plot is Test Scores. The number line ranges from 45 to 95. The whiskers range from between 45 and 50 to between 90 and 95. The box ranges from between 65 and 70 to a little less than 85 with a median between 75 and 80.

C.
The title of the box and whisker plot is Test Scores. The number line ranges from 45 to 95. The whiskers range from between 45 and 50 to between 90 and 95. The box ranges from 65 to 85 with a median of 70.

D.
The title of the box and whisker plot is Test Scores. The number line ranges from 45 to 95. The whiskers range from between 45 and 50 to between 90 and 95. The box ranges from between 65 and 70 to a little less than 85 with a median between 70 and 75.

Rubric: (1 point) The student selects the correct option (e.g., A).