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How Many Jeans?
Resource ID#: 70160
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to select a measure of center to compare data displayed in dot plots and to
justify their choice.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, dot plots, center, median, mean, mode, data distribution
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_HowManyJeans_Worksheet.docx
MFAS_HowManyJeans_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the How Many Jeans?
worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not select a measure of center based on the shapes of the distributions or the presence of outlie
Examples of Student Work at this Level
The student does not make any reference to the shapes of the distributions or the presence of outliers in the selec

Choose measures of center to represent each distribution rather than one measure to compare.

Suggest using the median because it will be the same for both classes.

Compare the number of data points and notice the outlier but does not mention a measure of center.

Suggest using the mean, "Because it will show the most difference between the two."

Not choose a measure of center but instead describes the shapes of the dot plots.

Select one of the dot plots as the best measure of center.
Questions Eliciting Thinking
Does it make sense to compare the mean of one distribution to the median of another?
What are measures of center? Do you know any examples of measures of center?
What did you mean by "it will show the most difference between the two"?
Which class has a mean and a median that are different? Why do you think this happens?
How does the distribution of the data affect the mean? The median?
Instructional Implications
If needed, review terminology associated with the shapes of distributions such as symmetric, normal, skewed, an
Provide opportunities for the student to calculate both the mean and the median of a variety of distributions. Incl
Next, replace one of the data points with an extreme outlier. Again, ask the student to identify the median and co
may be a better choice of a measure of center. Make clear that the shape of a distribution and the presence of out
Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since
unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data
Provide additional opportunities to select measures of center to represent and compare distributions. Ask the stu
Making Progress
Misconception/Error
The student selects a measure of center based on the shapes of the distributions but provides an incomplete justif
Examples of Student Work at this Level
The student:

Provides an adequate justification for using the median for Class A but says it should also be used for Cl

Correctly suggests using the median but does not clearly explain that the median is more resistant to outl
Questions Eliciting Thinking
What did you mean by "the plots are closer"? How did this affect your choice of measure of center?
You said the distribution for Class A is skewed. Why is the median a better choice when the data is skewed?
You said the distribution for Class A contains an outlier. Why is the median a better choice when the data contai
Instructional Implications
Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since
unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data
Provide additional opportunities to select measures of center to represent and compare distributions. Ask the stud
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student selects the median as a measure of center to compare the distributions and uses the shape of the dist
outliers.
Questions Eliciting Thinking
Can you explain why the mean is more affected by outliers than the median?
Instructional Implications
Challenge the student to create three small sets of data: one in which the mean is less than the median, one in wh
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
How Many Jeans? worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.S-ID.1.2:
Description
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. ★
Remarks/Examples:
In grades 6 – 8, students describe center and spread in a
data distribution. Here they choose a summary statistic
appropriate to the characteristics of the data distribution,
such as the shape of the distribution or the existence of
extreme data points.