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Given a relative frequency table, construct and interpret a segmented bar graph.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Frequency table
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In Algebra I, students selected appropriate methods to represent categorical data including bar graphs and segmented bar graphs. In Math for Data and Financial Literacy, students take data represented in a two-way frequency table and use this data to construct a segmented bar graph and interpret the data.- Instruction includes the use of problems with relevant, real-world contexts (MTR.7.1).
- Segmented Bar Graph
A segmented bar graph is used to compare two categories within a data set. Each bar will consist of all the data in that category. Each bar will be partitioned to show the different percentages of each type of data in that category. Each bar will show 100% of the data in that category (MTR.2.1).
- A person takes part in a medical trial that tests the effect of a medicine on a disease. Half the people are given medicine and the other half are given a placebo, which has no effect on the disease. The medicine has a 62% chance of curing someone. But people who do not get the medicine still have a 10% chance of getting well. There are 120 people in the trial and they all have the disease. Construct a two-way relative frequency table to summarize the data. Use a tree diagram to help organize the information. The two-way relative frequency table that summarizes the data is shown below.
- To construct the segmented bar graph, students can choose to have the categories as Gets Medicine and Gets Placebo or students can choose Gets Better and Doesn’t Get Better as the two categories. For this example, we will choose Gets Medicine and Gets Placebo as the comparative categories.
- To construct the segmented bar for Gets Better, students will need to determine the conditional relative frequencies for getting better with the condition that a person gets the medicine and for not getting better with the same condition. The two percentages together, should add up to 100%
(Gets Better | Gets Medicine) = 31/50 = 62%
(Doesn’t Get Better | Gets Medicine) = 19/50 = 38%
Students will repeat the process with the condition that a person gets the placebo.
(Gets Better | Gets Placebo) = 5/50 = 10%
(Doesn’t Get Better | Gets Placebo) = 45/50 = 90%
- Students will need to create a key to show which segment belongs to Gets Better and which segment belongs to doesn’t get better. This is typically done with different colors or markings for the segments.
Common Misconceptions or Errors
- Students may use the joint relative frequencies when segmenting the bars. In this case, the segments would not add up to 100%.
- Students may forget to make a key defining the segment pieces.
- Students may have trouble determining the conditional relative frequencies or may mix up the conditions.
Instructional Tasks
Instructional Task 1 (MTR.4.1, MTR.7.1, MTR.2.1)- A diabetes diagnostic test can sometimes lead to false negative and false positive results. A city is implementing a new diabetes diagnostic test for all its residents. Five percent of people in the city actually have the disease. The test has a 97% accuracy rating for positive results and a 7% false positive rate.
- Part A. Create a two-way relative frequency table to summarize the data.
- Part B. Use Part A to create a segmented bar graph representing the data.
- Part C. What do each of the joint frequencies mean in terms of the context?
- Part D. Would you recommend the city use the diabetes diagnostic? Why or why not?
Instructional Items
Instructional Item 1- The relative frequency table below describes risk factors for obesity associated with age.
- Use the relative frequency table above to create a segmented bar graph representing the data.
Related Courses
This benchmark is part of these courses.
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 - 2024, 2024 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Problem-Solving Task
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
Problem-Solving Task
Music and Sports:
This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.
Type: Problem-Solving Task
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
Problem-Solving Task
Music and Sports:
This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.
Type: Problem-Solving Task
