MA.7.DP.1.2

Given two numerical or graphical representations of data, use the measure(s) of center and measure(s) of variability to make comparisons, interpret results and draw conclusions about the two populations.

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.

General Information

Subject Area: Mathematics (B.E.S.T.)

Grade: 7

Strand: Data Analysis and Probability

Standard: Represent and interpret numerical and categorical data.

Date Adopted or Revised: 08/20

Status: State Board Approved

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
MA.6.DP.1.2

Next Benchmarks
MA.8.DP.1.1

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.
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.

Average Amount of Time on Homework Per Night (in minutes)

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 1
High 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.

Is a student more likely to go to a state or community college? Which choice has more variability?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.

1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))

1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

MA.7.DP.1.AP.2: Given two numerical or graphical representations of data in the same form, compare the mean, median or range of each representation.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Cranberry Counting:

Students are asked to assess the validity of an inference regarding two distributions given their box plots.

Type: Formative Assessment

TV Ages - 1:

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.

Type: Formative Assessment

TV Ages - 2:

Type: Formative Assessment

Overlapping Trees:

Students are asked to compare two distributions given side-by-side box plots.

Type: Formative Assessment

Lesson Plans

Foreign Trade Scenarios:

Students will utilize historical trade flow data (import and export) to interpret, create, and draw conclusions about foreign policy, specifically the World Trade Organization. Students will write a claim using the data to make suggestions regarding foreign trade import and export in this integrated lesson plan.

Type: Lesson Plan

Build a New School:

Students will calculate, interpret, and use measures of center and spread of different populations to determine in which city in Manatee County new schools should be built. Students will also use percentages to estimate the future population of school-aged children which will be used to determine where new schools should be built.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here: https://www.cpalms.org/cpalms/mea.aspx to learn more about MEAs and how they can transform your classroom.They resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator.

Type: Lesson Plan

Is My Backpack Too Massive?:

This lesson combines many objectives for seventh grade students. Its goal is for students to create and carry out an investigation about student backpack mass. Students will develop a conclusion based on statistical and graphical analysis.

Type: Lesson Plan

Original Student Tutorial

Math Models and Social Distancing:

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: Experts

Chronic Pain and the Brain:

Florida State researcher Jens Foell discusses the use of fMRI and statistics in chronic pain.

Type: Perspectives Video: Expert

fMRI, Phantom Limb Pain and Statistical Noise:

Jens Foell discusses how statistical noise reduction is used in fMRI brain imaging to be able to determine which specifics parts of the brain are related to certain activities and how this relates to patients that suffer from phantom limb pain.

Type: Perspectives Video: Expert

Histograms Show Trends in Fisheries Data Over Time:

NOAA Fishery management relies on histograms to show patterns and trends over time of fishery data.

Type: Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

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

Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.