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Clarifications
Clarification 1: Graphical representations are limited to histograms, line plots, box plots and stem-and-leaf plots.Clarification 2: The measure of center is limited to mean and median. The measure of variation is limited to range and interquartile range.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Box Plot
- Data
- Histogram
- Interquartile Range (IQR)
- Line Plot
- Mean
- Measures of Center
- Measures of Variability
- Median
- Range (of data set)
- Stem-and-Leaf Plot
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 6, students calculated and interpreted mean, median, mode and range, while in grade 7, they use those calculations to make comparisons, interpret results and draw conclusions about two populations. In grade 8, students will learn how to interpret the main features of line graphs and lines of fit.- Instruction includes cases where students need to calculate measures of center and variation in order to interpret them.
- Instruction includes having students collect their own data for analysis. Student interest in making comparisons assists with students making sense of the data to interpret comparisons (MTR.1.1, MTR.7.1).
- Students should not be expected to classify differences between data sets as “significant” or “not significant.”
- Data representations can be shown as a two-sided stem-and-leaf plot and multiple box plots on the same scale.
- Data representations should include titles, labels and a key as appropriate.
Common Misconceptions or Errors
- Some students may incorrectly believe a histogram with greater variability in the heights of the bars indicates greater variability of the data set.
- Students may not recognize when to use a stem-and-leaf plot or may not be able to read a two-sided stem-and-leaf plot.
- Students may not be able to explain their choice of the most appropriate measures of center and variability based on the given data.
- Students may think that the presence of one or more outliers leads to an automatic choice (median, IQR) for the measures of center and variation.
Strategies to Support Tiered Instruction
- Instruction includes explaining the difference between variability in the heights of the bars of histograms, and the actual variability of the data set.
- Teacher provides instruction on how to use different type of data displays to show two sets of data at the same time. Teachers co-construct an anchor chart explaining the different parts of each display with explanations on when and how to use each of them.
- For example, teacher can provide students with a two-sided stem-and-leaf plot with the “stem” in the middle and “leaves” on either side, each displaying the two data sets.
- For example, teacher can provide students with two line plots or two box plots on the same number line. Plots can be given in different colors to show the different data sets.
- For example, teacher can provide students with a two-sided stem-and-leaf plot with the “stem” in the middle and “leaves” on either side, each displaying the two data sets.
- Teacher provides instruction on which measure of center and variation should be used, making sure to include what to do when an outlier is present.
- Teacher facilitates discussion on the different measures of center and variability and how to know when to use each one. Use a graphic organizer to compare the different measures of center and variability to assist students in deciding when to use them.
- Instruction includes co-creating an anchor chart with different data displays containing visual representations and explanations of when and how to use them.
Instructional Tasks
Instructional Task 1 (MTR.1.1, MTR.7.1)A group of students in the book club are debating whether high school juniors or seniors spend more time on homework. A random sampling of juniors and seniors at the local high school were surveyed about the average amount of time they spent per night on homework. The results are listed in the table below.
- Part A. Calculate and compare the measures of center for the data sets.
- Part B. Calculate and compare the variability in each distribution.
- Part C. Does the data support juniors or seniors spending more time on homework? Explain your reasoning.
Instructional Items
Instructional Item 1High schools around the state of Florida were asked what percentage of students in their graduating class would be attending a state college and what percentage would be attending a community college. The results are provided in the graph below.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Experts
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
Teaching Idea
MFAS Formative Assessments
Students are asked to assess the validity of an inference regarding two distributions given their box plots.
Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.
Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.
Original Student Tutorials Mathematics - Grades 6-8
Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.
Student Resources
Original Student Tutorial
Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.
Type: Original Student Tutorial
Perspectives Video: Expert
The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?
Download the CPALMS Perspectives video student note taking guide.
Type: Perspectives Video: Expert
Problem-Solving Tasks
The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.
Type: Problem-Solving Task
This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.
Type: Problem-Solving Task
In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.
Type: Problem-Solving Task
This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.
Type: Problem-Solving Task
In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.
Type: Problem-Solving Task
