Mathematics · 6th Grade · Data Displays and Cumulative Review · Weeks 28-36

Interpreting Data Displays

Students will interpret various data displays, including dot plots, histograms, and box plots, to answer statistical questions.

• Common Core State Standards
• CCSS.Math.Content.6.SP.B.4
• CCSS.Math.Content.6.SP.B.5

About This Topic

Reading a graph is not the same as interpreting one. Interpreting data displays requires students to extract meaning , about shape, center, spread, and notable features , and connect that meaning to the context from which the data came. Students at this level work with dot plots, histograms, and box plots, each of which highlights different aspects of a distribution.

CCSS 6.SP.B.4 and 6.SP.B.5 ask students not only to read values from graphs but to describe what the overall distribution looks like and what measures of center and variability tell them. A major US curriculum goal at this level is statistical literacy , the ability to evaluate claims made from data and identify when a display is misleading. Students need practice reading scales critically and questioning the choices made in how data is presented.

Active learning strategies that involve argumentation and critique are well matched here. When students are asked to construct a narrative from a graph or to spot misleading design choices, they engage with data analytically rather than passively.

Key Questions

1. Critique how the scale of a graph can be used to mislead an audience.
2. Construct a narrative about a data set based on its graphical representation.
3. Evaluate the effectiveness of different data displays for different types of questions.

Learning Objectives

• Analyze dot plots, histograms, and box plots to identify the shape, center, and spread of a data distribution.
• Evaluate how the choice of scale and graph type can influence the interpretation of data.
• Construct a narrative that explains the meaning of a data set based on its graphical representation.
• Compare the effectiveness of dot plots, histograms, and box plots for answering specific statistical questions about a data set.

Before You Start

Data Collection and Organization

Why: Students need to be able to collect and organize data into tables before they can create or interpret graphical displays of that data.

Understanding of Basic Statistical Measures

Why: Students should have a foundational understanding of concepts like mean, median, and range to interpret the center and spread shown in various graphs.

Key Vocabulary

Dot Plot	A data display that uses dots above a number line to show the frequency of each value in a data set.
Histogram	A data display that uses bars to show the frequency of data points falling within specified intervals or bins.
Box Plot	A data display that shows the distribution of a data set using quartiles, median, minimum, and maximum values.
Scale	The range of values represented on the axes of a graph, which can be manipulated to emphasize or de-emphasize certain aspects of the data.
Distribution	The way data values are spread out or clustered, including their shape, center, and variability.

Watch Out for These Misconceptions

Common Misconception

A taller bar in a histogram always means more data values.

What to Teach Instead

Bar height represents frequency within that interval, which is true as long as all bins are equal width. With unequal bin widths, height alone is misleading. Examining histograms with deliberately varied bin widths during group work surfaces this limitation.

Common Misconception

The display format doesn't affect the conclusions you can draw.

What to Teach Instead

Different displays highlight different features. A box plot clearly shows the median and IQR but hides multi-modal patterns; a dot plot shows every value but clutters with large data sets. The 'best display for the question' investigation makes this concrete.

Active Learning Ideas

Gallery Walk: What's the Story?

Post six data displays (mix of dot plots, histograms, box plots) with context labels removed. Groups write a one-paragraph narrative about what each display shows , center, spread, shape, outliers , without being told what the data is about. Debrief compares narratives across groups.

40 min·Small Groups

Think-Pair-Share: Spot the Misleading Graph

Show students a histogram with a truncated y-axis that makes a small difference look dramatic. Pairs analyze the graph, identify the design choice that misleads, and redraw a fair version. Class discusses how scale choices influence perception.

25 min·Pairs

Inquiry Circle: Best Display for the Question

Groups receive three versions of the same data (dot plot, histogram, box plot) and a set of five interpretation questions. They determine which display answers each question most efficiently and explain their reasoning in writing.

40 min·Small Groups

Real-World Connections

• Market researchers use histograms to visualize customer demographics, helping companies understand age ranges and income levels to tailor product marketing for brands like Nike or Apple.
• Sports analysts examine box plots of player statistics, such as batting averages or points per game, to compare player performance across seasons or teams, informing draft picks or trade decisions.
• Urban planners might use dot plots to display the frequency of public transportation usage at different times of day, helping cities like Seattle or Denver optimize bus and train schedules.

Assessment Ideas

Exit Ticket

Provide students with two versions of the same data displayed on graphs with different scales. Ask: 'Which graph makes the difference between Group A and Group B seem larger? Explain why, referencing the scale.'

Discussion Prompt

Present a scenario, such as 'A local news report claims that most students in our school get less than 3 hours of sleep.' Show a histogram of student sleep data. Ask: 'Does this graph support the claim? How could the graph be changed to make the claim look stronger or weaker?'

Quick Check

Give students a box plot showing the heights of students in two different classes. Ask them to write one sentence comparing the typical height and one sentence comparing the spread of heights for the two classes.

Frequently Asked Questions

How do you interpret a box plot?

A box plot shows the five-number summary: the minimum and maximum (the whiskers), the first and third quartiles (the box edges), and the median (the line inside the box). The box width equals the IQR, and any points beyond the whiskers are potential outliers.

How can a graph be misleading?

Common misleading techniques include truncating the y-axis (making small differences look large), using unequal bin widths in histograms, or changing scale between two graphs that are meant to be compared. Critically evaluating scale choices is a core statistical literacy skill.

How does active learning help students interpret data displays?

Writing narratives from displays without context labels forces students to rely entirely on what the graph communicates, building genuine reading skill. Spot-the-misleading-graph activities train critical analysis rather than passive consumption. Both approaches are more effective than simply asking students to answer comprehension questions about pre-interpreted charts.

Which data display is best for showing the median?

A box plot directly shows the median as the line inside the box, making it the most efficient display for spotting or comparing medians. Dot plots can also show the median visually, but box plots are purpose-built for displaying the five-number summary.