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Data Displays and Distributions

Students organize quantitative data and interpret dot plots, histograms, stem-and-leaf plots, and box plots.

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Beginner 15–20 minutes Probability & Statistics

Probability & Statistics Page 1 of 8

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At a Glance

Data Displays and Distributions

Binder SectionProbability & Statistics

DifficultyBeginner

Estimated Time15–20 minutes

PrerequisitesNone

Essential Question

How can differences in distributions support a fair comparison between groups?

Build Understanding

A data display should reveal the shape of a distribution. Dot plots show every value, histograms group values into equal intervals, and box plots summarize data with the five-number summary.

Describe a distribution by its shape, center, spread, clusters, gaps, and outliers. Always read the scale and labels before drawing a conclusion.

Visual Model

4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

Choose a display that fits the data and question.
Use equal intervals in histograms.
A box plot shows minimum, Q1, median, Q3, and maximum.
Describe shape, center, spread, and unusual features.
A graph can mislead when its scale or intervals are distorted.

Click each word

Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Group A median 72,IQR 8; Group B median 80,IQR 9

B has higher center with similar spread.

Example 2

Difference in means is 6 while MADs are about 2

Difference is large relative to variability.

Ask and explain

Common Questions

Do histogram bars touch? Yes, because intervals represent continuous numerical ranges.

Does a box plot show every value? No; it summarizes a distribution.

Is every extreme value an outlier? No; use context or an outlier rule.

Notice and correct

Common Misconceptions

Comparing only maximum values

Use typical values and spread.

Ignoring unequal scales or sample sizes

Read axes and context carefully.

Learn Through Video

Watch, pause, and explain

Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.

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Now Playing

Box and Whisker Plots Explained - Math with Mr. J

1 Box and Whisker Plots Explained - Math with Mr. J 2 Stem-and-Leaf Plots - Math with Mr. J

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Practice until you can explain it

Move from a quick warm-up to guided practice, independent work, and deeper challenges.

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Warm-Up Guided Independent Challenge

Quick Start

Warm-Up

Warm-up 1

Two groups have equal medians but IQRs 4 and 15. Which is more consistent?

We Do

Guided Practice

Guided 1

For 2, 3, 3, 5, 8, the mode is 3 and range is 6.

Guided 2

Five-number summary 1, 4, 7, 10, 14 has IQR 6.

Guided 3

A long right tail describes a right-skewed distribution.

Guided 4

A histogram interval must not overlap the next interval.

Guided 5

A box plot with a longer right whisker suggests greater spread above Q3.

You Do

Independent Practice

Independent 1

Two groups have equal medians but IQRs 4 and 15. Which is more consistent?

Independent 2

Create and solve a second example with different values.

Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Create two distributions supporting a nuanced claim: one group has a higher center but also greater variability. Defend the wording.

IXL

Interpret Dot Plots

Open resource

IXL

Create Histograms

Open resource

IXL

Box Plots

Open resource

Khan Academy

Displaying and Comparing Quantitative Data

Open resource

DeltaMath

DeltaMath: Dot Plots and Histograms

Open resource

DeltaMath

DeltaMath: Box Plots

Open resource

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Success Criteria

Before you begin, I can…

I can identify the important information.
I can use accurate notation, labels, and units.
I can justify and verify my conclusion.

Question 1

What should happen before calculating?

Question 2

Which response gives the strongest evidence?

Question 3

What is an effective accuracy check?

Question 4

Why are units or labels important?

Question 5

What should a student do after finding an error?

Confidence Check

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Lesson Complete

Great job on Data Displays and Distributions!

You reviewed the lesson, practiced the skill, and completed the mastery check.

Next Lesson: Measures of Center and Spread → Back to Binder Topics

At a Glance

Learning Targets

Interactive Vocabulary

Worked Examples

Group A median 72,IQR 8; Group B median 80,IQR 9

Difference in means is 6 while MADs are about 2

Common Questions

Common Misconceptions

Watch, pause, and explain

Box and Whisker Plots Explained - Math with Mr. J

Ready to practice?

Practice until you can explain it

Warm-Up

Two groups have equal medians but IQRs 4 and 15. Which is more consistent?

Guided Practice

For 2, 3, 3, 5, 8, the mode is 3 and range is 6.

Five-number summary 1, 4, 7, 10, 14 has IQR 6.

A long right tail describes a right-skewed distribution.

A histogram interval must not overlap the next interval.

A box plot with a longer right whisker suggests greater spread above Q3.

Independent Practice

Two groups have equal medians but IQRs 4 and 15. Which is more consistent?

Create and solve a second example with different values.

Challenge & Real-World Practice

Nice work!

IXL

Interpret Dot Plots

Create Histograms

Box Plots

Khan Academy

Displaying and Comparing Quantitative Data

DeltaMath

DeltaMath: Dot Plots and Histograms

DeltaMath: Box Plots

Save today’s lesson and grow your MathBinder

Printable Resources

Interactive Notebook Printables

Recently Added

My MathBinder

Build a Review Packet

My Collected Lessons

Favorite This Lesson

Continue Learning

Your Binder Achievements

Learned. Watched. Practiced. Saved.

My Math Journal

How confident do you feel?

Complete the thought

What do you want to remember?

My Journal History

Ready to check your understanding?

Can you do this on your own?

Before you begin, I can…

What should happen before calculating?

Which response gives the strongest evidence?

What is an effective accuracy check?

Why are units or labels important?

What should a student do after finding an error?

How confident do you feel?

Your Results

Review and try again

Great job on Data Displays and Distributions!