# MA.6.DP.1.4

Given a histogram or line plot within a real-world context, qualitatively describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers and the range.

### Clarifications

Clarification 1: Refer to K-12 Mathematics Glossary (Appendix C).
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

• Cluster
• Data
• Histogram
• Line Plot
• Outlier
• Range

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 5, students interpreted numerical data from tables and line plots by determining the mean, median, mode and range. In grade 6, students extend their understanding of data interpretation by describing qualitatively the symmetry, skewness, gaps, clusters and outliers of line plots and histograms. Additionally, students will expand from whole-number data sets to rational-number data sets and to include histograms as a graphical representation. In grade 7, students compare two data sets to interpret and draw conclusions about populations.
• Instruction includes developing statistical questions that generate numerical data.
• Instruction includes the understanding that line plots are useful for highlighting clusters, gaps and outliers within a data set and show the shape of the distribution of a data set while displaying the individual data points. Likewise, students should understand that histograms are useful for highlighting clusters and gaps and shows the shape of the distribution of a data set without displaying the individual data points. Additionally, histograms help identify the shape and spread of the data set.
• Problem types include using a histogram’s or line plot’s symmetry, skewness, gap(s), cluster(s), outlier(s) or range to qualitatively describe the spread/distribution; qualitatively interpret the spread/distribution; or both qualitatively describe and interpret the spread/distribution.
• Instruction relates to MA.6.DP.1.5 in which students create histograms to represent sets of numerical data.
• When describing the distribution, students are not expected to use the term uniform. Instruction focuses on describing data as normal, skewed or bimodal.

• Within this benchmark, the expectation is not to identify skewness as positive, negative, left or right. Students are only expected to describe and interpret skewness within a data set generally. When describing spread of the distribution, students should be able to interpret whether the data set has a narrow range (less spread), wide range (more spread) or contains an outlier (MTR.4.1).

### Common Misconceptions or Errors

• Students may confuse bar graphs (categorical data) and histograms (numerical data).
• Students have difficulty understanding skewness and how that relates to data and its interpretation.

### Strategies to Support Tiered Instruction

• Teacher displays histograms and line plots, side by side and discusses with students by comparing and contrasting each one to assist students in understanding the difference between the two, and what information can be interpreted from each one.
• Teacher facilitates discussion on symmetry, skewness, gaps, clusters, outliers, and range with students, providing instruction when needed. Teacher provides additional examples for students to reference after instruction.
• Teacher displays a graph or other visual representation to show a real-world example will assist in students seeing data that is skewed.
• For example, showing a dot plot of the number of Electoral Votes states have will show data that is skewed. Then conversations can be had about what it means that most of the data points are to the left, and which states have the most votes.

Instructional Task 1 (MTR.4.1)

Provide students, either individually or whole group, the histogram below. Have the students slowly and closely observe the graphical representation for 2 minutes. While the students are doing this, have them write down as many observations and wonderings of the graph as they can. Have students share their thinking with a partner. Then as a class, create a cohesive description and interpretation of the histogram.

Instructional Task 2 (MTR.4.1)

The data set {3.25, 2.25, 0.5, 1.5, 1, 0.75, 4, 1, 2.25, 2, 1.5, 1.5, 0.75, 3, 4, 2} is the result of LaKeesha taking a survey of her class to find out how many hours each student spent on their phones on Tuesday. Describe the distribution by stating its symmetry, its range, any outliers, any clusters and any gaps.

### Instructional Items

Instructional Item 1
The line plot below shows the distribution of test scores in Mrs. Duncan’s math class.

• Part A. Describe the shape of the distribution. What does the shape of the distribution indicate about how students scored on the math test?
• Part B. Describe the spread by using the range and explain what the shape means in terms of the students’ scores on the math test.

*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.
1205010: M/J Grade 6 Mathematics (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))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.DP.1.AP.4: Given a histogram or a line plot, describe the physical features of the graph.

## Related Resources

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

## Formative Assessments

Quiz Mean and Deviation:

Students are asked to calculate measures of center and variability, identify outliers, and interpret the meaning of each in context.

Type: Formative Assessment

Florida Lakes:

Students are given a histogram and are asked to describe the variable under investigation and the number of observations.

Type: Formative Assessment

Select the Better Measure:

Students are asked to select the better measure of center and variability to describe each of two distributions of data.

Type: Formative Assessment

Math Test Center:

Students are asked to describe and compare the centers of two data sets given their dot plots.

Type: Formative Assessment

Pet Frequency:

Students are asked to describe the distribution of data given in raw form.

Type: Formative Assessment

Students are asked to describe and compare the spread of the distribution of two data sets given their dot plots.

Type: Formative Assessment

Math Test Shape:

Students are asked to describe the shapes of three distributions given their dot plots and to explain the shapes in terms of the context.

Type: Formative Assessment

## Lesson Plans

"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

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

Which is Better? Using Data to Make Choices:

Students use technology to analyze measures of center and variability in data. Data displays such as box plots, line plots, and histograms are used. The effects of outliers are taken into consideration when drawing conclusions. Students will cite evidence from the data to support their conclusions.

Type: Lesson Plan

How long did you study?:

Students will create and analyze histograms based on student study time when preparing for the Algebra EOC. Students will be given a set of data and guided notes

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

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

How do we measure success?:

Students will use the normal distribution to estimate population percentages and calculate the values that fall within one, two, and three standard deviations of the mean. Students use statistics and a normal distribution to determine how well a participant performed in a math competition.

Type: Lesson Plan

Centers, Spreads, and Outliers:

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

Type: Lesson Plan

Should Statistics be Shapely?:

Students will Interpret differences in shape, center, and spread of a variety of data displays, accounting for possible effects of extreme data points.

Students will create a Human Box Plot using their data to master the standard and learning objectives, then complete interactive notes with the classroom teacher, a formative assessment, and later a summative assessment to show mastery.

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

Advantages and Disadvantages of Dot Plots, Histograms, and Box Plots:

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

## Original Student Tutorial

Castles, Catapults and Data: Histograms Part 2:

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

Type: Original Student Tutorial

## 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

## Perspectives Video: Professional/Enthusiast

Normal? Non-Normal Distributions & Oceanography:

What does it mean to be normally distributed?  What do oceanographers do when the collected data is not normally distributed?

Type: Perspectives Video: Professional/Enthusiast

## MFAS Formative Assessments

Florida Lakes:

Students are given a histogram and are asked to describe the variable under investigation and the number of observations.

Math Test Center:

Students are asked to describe and compare the centers of two data sets given their dot plots.

Math Test Shape:

Students are asked to describe the shapes of three distributions given their dot plots and to explain the shapes in terms of the context.

Students are asked to describe and compare the spread of the distribution of two data sets given their dot plots.

Pet Frequency:

Students are asked to describe the distribution of data given in raw form.

Quiz Mean and Deviation:

Students are asked to calculate measures of center and variability, identify outliers, and interpret the meaning of each in context.

Select the Better Measure:

Students are asked to select the better measure of center and variability to describe each of two distributions of data.

## Original Student Tutorials Mathematics - Grades 6-8

Castles, Catapults and Data: Histograms Part 2:

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

## Student Resources

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

## Original Student Tutorial

Castles, Catapults and Data: Histograms Part 2:

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.