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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.
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Interactive Vocabulary

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Worked Examples

Example 1

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

1

B has higher center with similar spread.

Example 2

Difference in means is 6 while MADs are about 2

1

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.

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Comparing Data Distributions lesson and examples

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Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

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

Picture the dataUse the picture to organize what you know before you solve.
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2
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Guided Practice

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Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

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

Picture the dataUse the picture to organize what you know before you solve.
ABC

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture the dataUse the picture to organize what you know before you solve.
ABC

Choose how you want to work or answer.

4
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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.

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  • I can identify the important information.
  • I can use accurate notation, labels, and units.
  • I can justify and verify my conclusion.
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Question 1

What should happen before calculating?

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Question 2

Which response gives the strongest evidence?

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Question 3

What is an effective accuracy check?

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Question 4

Why are units or labels important?

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What should a student do after finding an error?

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