Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70227
Conditional Relative Frequency
Students are asked to use a two-way frequency table to interpret two different conditional relative frequencies.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, two-way frequency table, conditional relative frequency, marginal frequency, marginal relative
frequency, categories, data, rows, columns, cells, variables
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ConditionalRelativeFrequency_Worksheet.docx
MFAS_ConditionalRelativeFrequency_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 problems on the Conditional Relative Frequency worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is not able to interpret conditional relative frequencies of data in a two-way table.
Examples of Student Work at this Level
The student’s explanation of conditional relative frequency is unclear or incorrect. For example, the student:
Writes the same explanation for both conditional relative frequencies.
page 1 of 4 Converts each conditional relative frequency to a decimal or percent without further interpretation.
Incorrectly describes one or both relative frequencies.
Questions Eliciting Thinking
What is the meaning of conditional relative frequency?
The conditional relative frequencies are given as fractions. What does the numerator of each fraction represent? The denominator?
Where are the values of the denominator of each fraction located in the table? How can this location help you understand its meaning?
In the table, the value of 17 combines which two categories? What does the value of 50 represent in the table? Can you use the structure of a fraction to interpret how
these two categories are related?
What does the value of 29 represent in the table? Can you use the structure of a fraction to interpret the relationship between 17 and 29?
Instructional Implications
Provide instruction on the structure of two-way frequency tables. Assist the student in identifying the two variables described in the context (e.g., gender and
vegetarianism) and the number of levels of each variable [e.g., two levels of gender (male and female) and two levels of vegetarianism (vegetarian and non-vegetarian)].
Provide the student direct instruction on interpreting marginal, joint, and conditional relative frequencies for data in two-way tables. Remind the student that a conditional
frequency represents a number in a cell from the body of the table out of a row or column total. Ask the student to identify the cell containing 17 and its row total of 50.
Guide the student to use the appropriate column and row titles and the context of the data to explain the meaning of
. Do the same for
.
Provide practice writing marginal, joint, and conditional relative frequencies for data in two-way tables. Assist the student with interpreting marginal, joint, and conditional
relative frequencies when given in fraction form. Tell the student to use the relationship between the numerator and denominator of a fraction to guide the word
arrangement for a clear and concise response. Give feedback as necessary.
Making Progress
Misconception/Error
The student’s interpretation lacks specificity.
Examples of Student Work at this Level
The student indicates an understanding of the conditional relative frequencies in the context of the data but omits an important piece of information in his or her
interpretation. For example, the student:
Does not reference the actual values in the conditional relative frequencies when describing them.
Does not explain the meaning of the numerator or the denominator.
page 2 of 4 Provides a correct interpretation but makes errors when converting fractions to percents.
Questions Eliciting Thinking
How did you determine your interpretation? Which part of the table did you use?
How does understanding the structure (the numerator and denominator) of a fraction help you answer these questions? What does the numerator of a fraction represent?
The denominator?
Your answer is somewhat correct, but can you refine it or describe it more clearly and concisely?
What does the value of 17 represent in the table? Which value of 50 in the table do you think best relates to the value of 17?
Instructional Implications
Ask the student to identify the two categories related by the cell with an entry of 17. Next, ask the student to identify the values of 50 in the table and to choose the
value in the same row or column as 17. Finally, remind the student to use wording that supports the meaning of each of these values when interpreting the conditional
relative frequency.
Remind the student that writing a clear and concise response starts with using the wording of the question. For example, guide the student to describe the meaning of the
relative frequencies as: The conditional relative frequency of
is the number of (the category related to the numerator) out of (the category related to the
denominator).
Provide practice writing the marginal, joint, and conditional relative frequencies for data in two-way tables. Assist the student with interpreting marginal, joint, and
conditional relative frequencies when given in fraction form. Tell the student to use the relationship between the numerator and denominator of a fraction to guide the
word arrangement for a clear and concise response. Give feedback as necessary.
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 interprets the relative frequencies as follows:
The conditional relative frequency of
means that out of the 50 females surveyed, 17 of them are vegetarians.
The conditional relative frequency of
means that out of the 29 vegetarians surveyed, 17 of them are females.
Questions Eliciting Thinking
Can you interpret the meaning of
?
?
What if the sample size had not been 100? Would that change how you determine the relative frequencies?
Instructional Implications
Provide the student with data presented in a two-way table with a sample size that is not easily converted to a percent and with unequal row totals and unequal column
totals. Ask the student to consider how to calculate relative marginal and joint frequencies (i.e., what values should serve as denominators for each relative frequency).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Conditional Relative Frequency worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
page 3 of 4 District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.S-ID.2.5:
Description
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the
context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and
trends in the data. ★
page 4 of 4