Double Plot Duel Slides Double Plot Duel
Comparing Populations with Box and Whisker Plots
7th-8th Grade Math Data Analysis
Quick Heat Warm-up
Who had the better season? Compare the points per game for these two rivals:
Player A
12, 14, 15, 15, 16, 17, 18, 32
Player B
18, 19, 19, 20, 20, 21, 22, 23
Think: Which player is more consistent? Who has the highest potential?
Mastering the Plot
10 Minutes
Embedded media
Guiding Question:
If we drew two of these plots stacked vertically, what comparisons could we make instantly?
Mission: Battle of the Brands
1
Analyze
Calculate the 5-Number Summary for Brand A and Brand B batteries.
2
Plot
Create two stacked box plots on the same number line for direct comparison.
3
Argue
Write a recommendation based on consistency (IQR) and peak performance.
Check for outliers before you start drawing!
The Closure Debate
Does a higher maximum make a brand better if the median is lower?
Be prepared to share your argument with the class!
Battery Battle Data Sheet Battery Battle: Data Sheet
Tech Lab Comparative Testing Data #882-B
Experimental Data
Scenario
A tech review company tested 12 batteries from two different brands: Brand Alpha and Brand Omega. They measured the "Active Life" of each battery in hours under a heavy load (gaming console controller). Use this data to determine which brand is the superior choice for consumers.
Brand Alpha
Life in Hours (n=12)
22
24
25
25
26
26
27
27
28
29
30
32
Brand A Notes: Marketed as "The Reliable Choice." Users report consistent performance across various devices.
Brand Omega
Life in Hours (n=12)
18
20
22
23
24
25
27
28
32
35
42
45
Brand B Notes: Marketed as "Maximum Power." Users mention that some batteries last forever, but others die quickly.
Next Steps
Transfer these numbers to your Graphing Sheet .
Calculate the 5-number summary (Min, Q1, Med, Q3, Max) for both.
Check for outliers using the formula: \( [Q1 - 1.5(IQR), Q3 + 1.5(IQR)] \).
Plot both sets of data on the shared number line.
Battery Battle Lab Sheet Battery Battle: Lab Report
Statistical Analysis & Visual Comparison
Student Name: __________________________
Date: __________________________
1. The Five-Number Summary
BRAND ALPHA
Sorted Data (Smallest to Largest)
Transfer data from sheet here...
Minimum:
Maximum:
Q1 (Lower):
Q3 (Upper):
MEDIAN (Q2):
IQR:
Outlier Check (Show Work)
BRAND OMEGA
Sorted Data (Smallest to Largest)
Transfer data from sheet here...
Minimum:
Maximum:
Q1 (Lower):
Q3 (Upper):
MEDIAN (Q2):
IQR:
Outlier Check (Show Work)
2. Double Box Plot Visualization
BRAND ALPHA
BRAND OMEGA
15 20 25 30 35 40 45
Active Life (Hours)
Battery Battle Argument Template The Final Recommendation
Consumer Report: Battery Efficiency Analysis
Investigator: __________________________
Date: __________________________
The Critical Decision:
Based on your statistical analysis and the stacked box plots you created, which battery brand should the tech company recommend to its customers? Support your answer using Median , Consistency (IQR) , and Maximum Performance .
Step 1: The Claim
I recommend __________________________________ as the superior brand because
Step 2: Statistical Evidence
Comparing Medians:
Comparing Consistency (Interquartile Range - IQR):
Comparing Extremes (Maximums and Outliers):
Step 3: Synthesis
Why does your chosen data point outweigh the others? (e.g., Why is a consistent median better than a high maximum?)
Double Plot Duel Teacher Guide Teacher Guide: Double Plot Duel
Instructional Support & Answer Key
REF-ID: MATH-78-BATT
Learning Objectives
Calculate 5-number summaries for large datasets.
Identify outliers using the \( 1.5 \times IQR \) rule.
Construct and interpret stacked (double) box plots.
Argue a claim using statistical evidence (median vs. spread).
Lesson Pacing (50 min)
Warm-up 5 min
Video & Discussion 10 min
Data Analysis & Plotting 15 min
Argument Writing 10 min
Closure / Share-out 10 min
Key Instructional Moments
The Warm-up
Students often focus on the "highest number." Point out that Player A has a high outlier (32) but Player B has a much higher median (20 vs 15.5). Ask: "Who would you want on your team for a championship game?"
The Video
Pause at 12:12.
Ensure students understand that the whisker goes to the next highest actual data point within the boundary, not the boundary itself.
Differentiation
For students struggling with calculations, provide a "Cheat Sheet" for the outlier formula. For advanced students, ask them to calculate the percentage of data within the box (50%) vs the whiskers.
Master Data Key
Brand Alpha
Sorted: 22, 24, 25, 25, 26, 26, 27, 27, 28, 29, 30, 32 Min: 22 Q1: 25 Median: 26.5 Q3: 28.5 Max: 32 IQR: 3.5 Outliers: None
Brand Omega
Sorted: 18, 20, 22, 23, 24, 25, 27, 28, 32, 35, 42, 45 Min: 18 Q1: 22.5 Median: 26 (25+27)/2 Q3: 33.5 Max: 45 IQR: 11 Outliers: None (Range: 6 - 50)
The Conflict
Alpha has a higher median (26.5) and is much more consistent (small IQR).Omega has a lower median (26) but a much higher maximum (45).consistency/reliability (Alpha) or peak performance/potential (Omega).
