# MA.7.DP.1.5

Given a real-world numerical or categorical data set, choose and create an appropriate graphical representation.

### Clarifications

Clarification 1: Graphical representations are limited to histograms, bar charts, circle graphs, line plots, box plots and stem-and-leaf plots.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Bar Graph
• Box Plot
• Categorical
• Data Circle
• Graph
• Histogram
• Line Plot
• Stem-and-Leaf Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students created box plots and histograms to represent numerical data. In grade 7, students must choose and create an appropriate graphical representation for a given numerical or categorical data set. In grade 8, students will construct a scatter plot or a line graph for a given set of bivariate numerical data.
• Students were introduced to bar charts (bar graphs) in grade 3, students may need to be reintroduced to this graphical representation.
• Graphical representations of categorical data sets are helpful for showing trends that can be analyzed and making comparisons of categories, among different items, or items over time periods. They visually show the mode of the data and, at a quick glance, show categories in a set of data that dominate others. Depending on the graphical representation chosen, either the frequency (number of items) or relative frequency (percentage) for each category can be illustrated.
• Histograms (for numerical data) and box plots (for categorical data) work well in grouping large sets of data to be easily compared, but do not allow viewers access to each individual data point if needed for other calculations such as the mean.
• Circle graphs are not ideal when too many categories are included as it is difficult to distinguish the difference in sizes of the sectors. Bar graph (or bar charts) make a similar comparison but the heights of the bars make the comparison more easily distinguishable.
• Stem-and-leaf plots and line plots are useful in displaying the shape of a numerical data set, easily identifying the mode and outliers, and they contain all of the values in the data set allowing for additional calculations such as the mean. They are not ideal when there is a large volume of data since it is time consuming to create and becomes difficult to read or interpret.

### Common Misconceptions or Errors

• Students may not distinguish between histograms (numerical data) and bar charts, also called bar graphs (categorical data).

### Strategies to Support Tiered Instruction

• Instruction includes displaying histograms and bar charts side by side and allow students to compare and contrast each one to help them understand the difference between the two, and what information we can learn from each one.
• Teacher provides a graphic organizer for each type of data display for students to reference in the future.
• Teacher co-creates examples of both bar graphs and histograms with students, explaining step-by-step how to create them and how/why they are different.

The following data shows the grams of protein in 21 protein bars.
{12, 14, 11, 8, 10, 8, 14, 8, 8, 12, 10, 12, 15, 11, 15, 20, 10, 15, 12, 21, 20}
• Part A. Create two different graphical representations of the data using histograms, bar charts, circle graphs, line plots, box plots or stem-and-leaf plots.
• Part B. Compare and contrast the two displays and determine which is more appropriate. Explain your reasoning.

### Instructional Items

Instructional Item 1
Select an appropriate type of display for each of the following situations.
• the salaries of all 40 employees at a small company
• the salaries of all 250 people at a mid-sized company
• the distribution of colors in a bag of colored candies
• the number of siblings students in the 7th grade class have

*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))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 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.5: Given a data set, select an appropriate graphical representation (histogram, bar chart, or line plot).

## Related Resources

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

## 3D Modeling

Wind Farm Design Challenge:

In this engineering design challenge, students are asked to create the most efficient wind turbine while balancing cost constraints. Students will apply their knowledge of surface area and graphing while testing 3D-printed wind farm blades. In the end, students are challenged to design and test their own wind farm blades, using Tinkercad to model a 3D-printable blade.

Type: 3D Modeling

## Lesson Plans

The Watergate Effect part 3:

Students will create a circle graph to display categorical data of the public presidential approval rates after the Supreme Court Case United States v. Nixon. Students will graph results independently and compare them to the circle graphs created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926) and the Watergate Effect Part 2 Lesson (Resource ID#: 210122) to discuss the trend of the data over the entirety of the Supreme Court case.

Type: Lesson Plan

The Watergate Effect part 2:

Students will create a circle graph to display categorical data of the public presidential approval rates during the Supreme Court Case United States v. Nixon. Students will graph results in pairs/groups and compare them to the circle graph created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926).

Type: Lesson Plan

The Watergate Effect Part 1:

Students will create a circle graph to display categorical data of the public presidential approval rates of Richard Nixon before the Supreme Court Case United States v. Nixon. Students will calculate percentages and central angle degrees to graph results in pairs/groups and analyze the results in this integrated lesson plan.

Type: Lesson Plan

Budgeting and Decision-Making: Integrating Math and Civics:

This lesson will help students understand the concept of percentages within the context of government budgets. Students will explore how percentages are used to allocate funds in government budgets and how they can be effectively communicated using graphs. The lesson will involve collaborative learning, discussions, and problem-solving to foster critical thinking and application of math concepts in a civics context.

Type: Lesson Plan

Understanding Taxation and Civic Obligation:

Students will use their knowledge of percentages to calculate federal income tax and local sales tax. They will explore the obligation of citizens to pay taxes and how taxes fund public services. Students will evaluate different tax models by comparing percentages of income taxed at different income levels.

Type: Lesson Plan

Analyzing Government Spending: Integrating math & civics:

Students will practice their skills in interpreting data and creating graphical representations in this integrated civics lesson. Students will apply graphing skills to analyze government spending data and reflect on the importance of mathematics in communicating complex numerical information visually so the public can better stay informed.

Type: Lesson Plan

Graphing Local Voting Data:

This is lesson 3 in a mini unit of 3 lessons. Students will analyze voting data from a Florida county. Students will use the given data to choose and create an appropriate graphical representation.

Type: Lesson Plan

Graphing Data:

This is lesson 2 in a mini unit of 3 lessons. Students will analyze data collected from students, teachers, and principals to decide whether cell phone usage should be allowed in the classroom. They will be receiving data from fictional surveys of teachers and principals. Students will use the given data to choose and create an appropriate graphical representation.

Type: Lesson Plan

Introduction to Voting and Graphing Data:

The students will vote on whether cell phones should be allowed in the classroom or not. They will use this data to select the appropriate way of graphing the results. The teacher will give sample data from other teachers and principals for students to review. The correlation will be relating students to local voting in this integrated lesson plan.

Type: Lesson Plan

Clean the pier- To fish or not to fish?:

Students will examine the impact humans can have on the water quality at a popular public fishing pier and ways that citizens can interact with the government to address cleaning the pier in this integrated MEA. Students will analyze the revenue from the fishing pier, peak visiting times, and amounts of marine debris accumulated to determine the pros/cons of closing the fishing pier more frequently to clean the marine debris. Students will research which government agency must be contacted with a proposal.

Type: Lesson Plan

Students will compile the data gathered from measuring their resting heart rates and heart rates after exercising into box plots. Using these displays, they will analyze the data's center, shape, and spread.

Type: Lesson Plan

Bowling for Box Plots:

Students will learn about the effects of an outlier and interpret differences in shape, center, and spread using a bowling activity to gather data. The students will learn to score their games, report their scores, and collectively measure trends and spread by collaborating to create a box plot. They will analyze and compare box plots, and determine how much of an effect an extreme score (outlier) can have on the overall box plot of the data.

Type: Lesson Plan

"What's My Grade" is a lesson that will focus on a sample student's grades to demonstrate how a final grade is calculated as well as explore possible future grades. Students will create the distributions of each grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing the center and spread of two or more different data sets.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

Type: Lesson Plan

Which One: Box plot, Dot Plot, or Histogram?:

Students will be asked to obtain data and create a human box plot, which will be analyzed and explained using statistical terms. Students will then understand the differences and advantages to using the box plot, histogram, and dot plot. Students will also practice selecting the most appropriate graphical representation for a set of data.

Type: Lesson Plan

The Distance a Coin Will Travel:

This lesson is a hands-on activity that will allow students to collect and display data about how far different coins will travel. The data collected is then used to construct double dot plots and double box plots. This activity helps to facilitate the statistical implications of data collection and the application of central tendency and variability in data collection.

Type: Lesson Plan

How many licks does it take to get to the center?:

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

Type: Lesson Plan

Birthday Party Decisions:

Students will create and compare four different boxplots to determine the best location for a birthday party.

Type: Lesson Plan

Outliers in the Outfield – Dealing With Extreme Data Points:

Students will explore the effects outliers have on the mean and median values using the Major League Baseball (MLB) salary statistics. They will create and compare box plots and analyze measures of center and variability. They will also be given a set of three box plots and asked to identify and compare their measures of center and variablity.

Type: Lesson Plan

This lesson allows students to have a hands-on experience collecting real-world data, creating graphical representations, and analyzing their data. Students will make predictions as to the outcome of the data and compare their predictions to the actual outcome. Students will create and analyze line plots, histograms, and box plots.

Type: Lesson Plan

A Walk Down the Lane:

Students will collect data, and create box plots. Students will make predictions about which measurement best describes the spread and center of the data. Students will use this information to make predictions.

Type: Lesson Plan

How Old are the Players?:

For this lesson, students will research the ages of players on two basketball teams. They will find the five-number summary, the mean, and determine if there are outliers in the data set. Two box plots will be created and the measures of center and variation analyzed.

Type: Lesson Plan

The students will compare the effects of outliers on measures of center and spread within dot plots and box plots.

Type: Lesson Plan

Baking Soda and Vinegar: A statistical approach to a chemical reaction.:

Students experiment with baking soda and vinegar and use statistics to determine which ratio of ingredients creates the most carbon dioxide. This hands-on activity applies the concepts of plot, center, and spread.

Type: Lesson Plan

Homework or Play?:

Students will be given data and then plot the data using a graphical method of choice (dot plot, bar graph, box plot, etc.) The students will work in groups and then analyze and summarize the data.

Type: Lesson Plan

Sweet Statistics - A Candy Journey:

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

Type: Lesson Plan

Exploring Box plots:

This lesson involves real-world data situations. Students will use the data to create, explore, and compare the key components of a box plot.

Type: Lesson Plan

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Who's Better?--Using Data to Determine:

This lesson is intended for use after students are able to construct data plots (histograms, line plots, box plots). Students are tasked with not only constructing data plots, but also matching data plots to data sets. In the summative assessment, students are given two data sets and asked to select which of three data plots (histogram, line plot, or box plot) would best be used to compare the data. After choosing and constructing their plot, students are then tasked with forming a conclusion based on the plots they have constructed.

Type: Lesson Plan

Is It a Guess or Statistics?:

This lesson teaches random sampling which leads to making inferences about a larger group or population. Students will determine the best measure of center to use for a data set. Students will collect data, select a data display and then analyze the data.

Type: Lesson Plan

5E Natural Selection Module:

This resource uses a variety of techniques to address the factors that contribute to natural selection. Included in the lesson is a hook to engage students, a weblab exercise, a poster activity for expression and a hands-on simulation.

Type: Lesson Plan

Students will compare the advantages and disadvantages of dot plots, histograms, and box plots. During this lesson, students will review the statistical process and learn the characteristics of a statistical question; whether it be numerical or categorical. Students will apply the information learned in a project that involves real-world issues and make an analysis based on the data collected.

Type: Lesson Plan

Inferences:

This lesson shows students how to conduct a survey and display their results. The lesson takes the students through:

1. What is a statistical question?
2. General population versus sample population.
3. What is a hypothesis?
4. What is a survey?
5. How to make inferences.

Type: Lesson Plan

Box Plots:

An introduction lesson on creating and interpreting box plots.

Type: Lesson Plan

Speed Trap:

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Speed Trap:

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.