Data Duel Slides Data Duel
Comparing Distributions & Overlap
Tier 2 Intervention • Grade 7 Statistics
The Big Question
How can we tell if two groups are actually different, or if their results just happen to overlap?
Scenario A
High Overlap
The groups look mostly the same.
Scenario B
Low Overlap
The groups look very different.
Visual Overlap
Lots of Overlap
The centers are close together. The distributions "hide" each other.
Little Overlap
The centers are far apart. There is a clear gap or shift.
High Overlap
Low Overlap
The Calculation Secret
We measure the distance between the Centers (Mean or Median) relative to the Variability (MAD).
THE FORMULA
\[ \frac{\text{Difference in Means}}{\text{Mean Absolute Deviation (MAD)}} \]
~1
Significant Overlap
~2
Moderate Separation
3+
Little Overlap
MAD Quick Review
What is MAD?
The average distance between each data point and the mean.
Why use it?
It tells us if the data is "clumped together" or "spread out."
The 3 Steps
1 Find the Mean
2 Find distance from mean for each point
3 Average those distances
Duel Time!
Grab your lab reports. We're going to compare two datasets and find the overlap ratio.
Overlap Lab Worksheet Overlap Lab Report
Topic: Comparing Distributions (7.SP.B.3)
STUDENT:
DATE:
Mission Objective
Determine if two groups are significantly different by analyzing their overlap and calculating the center-to-variability ratio.
Case 1: The Training Grounds
Two teams recorded their scores. Look at the dot plots below. Team A is Blue, Team B is Orange.
012345678910
M
M
Scale: 0 to 10. "M" indicates the mean of the group.
1. Look at the plots. How much overlap do you see?
None
Some
Lots
2. What is the difference between the Means?
SCIENTIFIC OBSERVATION
Shade the area where the two distributions overlap. If there is no overlap, explain why you think they are different.
Case 2: The MAD Method
Two gardening clubs grew tomatoes. We need to find the overlap ratio.
Club A (Mean = 12 oz)
Variability Data
Distance from mean: 2, 1, 0, 1, 2
Calculate MAD A:
Club B (Mean = 18 oz)
Variability Data
Distance from mean: 2, 1, 0, 1, 2
Calculate MAD B:
STEP-BY-STEP
1. Difference in Means
18 - 12 = _____
/
2. Common MAD
_____
Ratio = _____
Conclusion
Based on your ratio, how much overlap do these groups have? (Circle one)
Low Ratio (~1) High Overlap
Med Ratio (~2) Moderate Overlap
High Ratio (3+) Low Overlap
Case 3: Box Plot Analysis
Recall: Box plots show the distribution through medians and quartiles.
Group A
Group B
How much overlap is there between the two "boxes" (middle 50%)?
Data Detective Guide Data Detective Guide
Teacher Facilitation • Grade 7 Tier 2 Intervention
Standard 7.SP.B.3
Instructional Focus
This lesson addresses the core concept of comparing distributions. Students often struggle to move beyond "one group has higher numbers." This intervention scaffolds the informal visual assessment of overlap and the more formal calculation of the difference in centers relative to variability .
Common Misconception
Students may think any difference in means indicates a "significant" difference. Remind them that if the data is highly spread out (high MAD), the difference in means might just be "noise."
Small Group Tips
Use color-coded highlighters (Blue/Orange) to match the worksheet and slides.
Physical "Overlay": Print two dot plots on separate transparencies. Slide them together to show "None" vs "Lots" of overlap.
Hand-over-hand MAD calculation support for students with dyscalculia.
Lesson Delivery Steps
1
The "Sliding Plots" Hook
Use Slide 3. Ask students: "If these were two groups of kids jumping, could you easily tell who is on which team?" If they are mixed up (high overlap), the team doesn't matter much. If they are separated (low overlap), the team makes a big difference.
2
The "Difference over MAD" Ratio
Explain that MAD is our "measuring stick." If the gap between means is 6 oz and the MAD is 2 oz, the gap is "3 MADs wide." This is a big gap! If the gap is 6 oz but the MAD is 6 oz, the gap is only "1 MAD wide." This is a small gap.
3
Guided Practice (Worksheet)
Work through Case 2 carefully. Many students will need help with the arithmetic of MAD. Use the provided "distance from mean" numbers to save time and focus on the division and interpretation .
Master Answer Key
Case 1: Training Grounds
Overlap: None (the dots are completely separated).Difference in Means: 7 - 3 = 4 units.Observation: Students should note the gap between the highest point of A and lowest of B.
Case 2: The MAD Method
MAD Calculations:
Club A: (2+1+0+1+2) / 5 = 1.2 oz
Club B: (2+1+0+1+2) / 5 = 1.2 oz
Ratio Calculation:
Difference in Means: 18 - 12 = 6
Ratio: 6 / 1.2 = 5
Data Duel Exit Ticket Exit Ticket
Data Duel Mastery Check
Name
Date
1 Visual Overlap
Look at the two distributions below. How would you describe their overlap?
No Overlap
Some Overlap
Lots of Overlap
2 Calculating the Ratio
Group A Mean: 40 Group B Mean: 50
Common MAD: 5
Show your ratio calculation:
(Diff in Means) / MAD
3 Interpretation
If a ratio is 0.5 , what does that tell you about the overlap of the two groups?
