Distribution Duel Slides Distribution Duel
Comparing Data with Precision
Tier 2 Intervention
The Mission
How can we tell if the difference between two groups is real or just random?
Look for...
Visual Overlap
Measure...
Distance Between Centers
Step 1: The Eye Test
High Overlap
The groups are very similar. The difference might not be significant.
Low Overlap
The groups are distinct. One group clearly performs differently.
Low Overlap = Clear Difference
Step 2: Compare Centers
We find the distance between the means (averages).
\[ \text{Distance} = \text{Mean}_1 - \text{Mean}_2 \]
Group 1 Mean
12 ft
Group 2 Mean
10 ft
Distance
2 ft
The MAD Ratio
Is a 2 ft difference big? It depends on how spread out the data is!
We use the Mean Absolute Deviation (MAD) to see if the gap is truly large.
The Golden Formula
\[ \frac{\text{Distance between Means}}{\text{MAD}} \]
If the result is 2 or more, the difference is very noticeable!
Quick Challenge
Practice Problem #1
Distance
6 units
MAD
2 units
Ratio
3.0
The difference between centers is 3 times the variability!
That's a massive difference!
Dot Plot Duel Worksheet Dot Plot Duel
Small Group Activity • Fitness Lab
Name:
Date:
Lab Mission
The Jump Test
Two groups of students tested a new pair of "Mega-Bounce" sneakers. Does the new technology actually help students jump further than the "Standard" sneakers? Use the data below to find out!
S Standard (inches)
10 11 12 12 13 13 14 15
M Mega-Bounce (inches)
13 14 15 15 16 16 17 18
Lab Bench
Stacked Dot Plots
Mega-Bounce Performance
910111213141516171819
Standard Performance
910111213141516171819
Lab Report Analysis
Visual Overlap Check
High (The groups look the same)
Moderate (Some dots shared)
Low (Groups are far apart)
Calculating the Gap
Mega Mean
Standard Mean
Difference
Step 3: Variability Test
The Mean Absolute Deviation (MAD) for our jump test is 1.5 inches. How many times does the MAD fit into the gap you calculated above?
Gap Distance
÷
MAD
1.5
=
The Multiple
Final Verdict:
Is the difference significant? (Hint: A multiple of 2 or more is a clear difference!)
Data Detective Exit Ticket Data Detective Check
Progress Monitoring • 7.SP.B.3
Student Name:
Date:
Scenario: A scientist is comparing the battery life of two phone brands.Brand A Mean: 15 hours • Brand B Mean: 12 hoursMean Absolute Deviation (MAD): 1.5 hours
1
What is the distance between the mean battery life of Brand A and Brand B?
Answer here
2
The distance between the means is how many times the MAD?
Show your division here
3
Based on your answer to Question 2, how much visual overlap would you expect to see on a dot plot?
A lot of overlap (The groups are very similar)
Very little overlap (The groups are very different)
4
Why is it important to compare the "gap" to the "MAD" instead of just looking at the gap alone?
Score
/ 4
Mastery
Distribution Coach Guide Distribution Coach
Facilitation Guide • Tier 2 Intervention
Objective
Students will informally assess overlap and express the difference in means as a multiple of the Mean Absolute Deviation (MAD).
Standard
CO 7.SP.B.3: Express the difference between centers as a multiple of a measure of variability.
Intervention Workflow
Phase 1
5 Mins
The Visual Hook
Use the Distribution Duel Slides . Focus on the concept of "The Eye Test."
Prompt: "If I move these two groups further apart, is there more or less overlap?"Key Concept: Low overlap usually means a significant difference.
Phase 2
15 Mins
Hands-On Duel
Transition to the Dot Plot Duel Worksheet . Students plot data for Standard vs. Mega-Bounce shoes.
Support: Help students find the "balance point" (mean) for each set visually before calculating.Calculation: Use a physical ruler or finger to show the "gap" between means.
Phase 3
10 Mins
The MAD Multiple
Introduce the ratio: Gap ÷ MAD.
Metaphor: "The MAD is our measuring stick. How many sticks can we fit in the gap?"Guideline: A multiple of 2 or more is usually considered a "large" difference.
Coaching Tips for Tier 2
Common Misconception
Students think a gap of "3 units" is always large. Remind them that if the data is spread out (large MAD), 3 units might be tiny!
Vocabulary Support
Variability = How messy or spread out the dots are.
Worksheet Answer Key (Sneaker Test)
Standard Mean: 12.5 Mega Mean: 15.5 Gap: 3.0 Multiple of MAD (1.5): 2.0
