Whisker Analysis Answer Keys Answer Keys
Reading the Whiskers • Teacher Resource
Confidential Teacher Key
1. Comparing Test Scores Activity Sheet
5-Number Summary (Class B)
Min: 70
Q1: 77.5
Median: 81.25
Q3: 85
Max: 92.5
Interquartile Range (IQR)
Class A: 17.5 (82.5 - 65)
Class B: 7.5 (85 - 77.5)
Most Consistent:
Class B (Smaller IQR indicates data is more tightly clustered).
Typical Performance
Class B has the higher typical score (81.25) compared to Class A (73.75). The entire middle 50% of Class B is above Class A's median.
Consistency Observation
It suggests that the vast majority of Class B students (at least 75%) scored higher than 50% of the students in Class A. Class B is much more reliable in its performance.
2. Box Plot Analysis Lab Worksheet
Case Study 1: Battery Endurance
Analysis A: Model X. Its Q3 is ~19.1h, but its maximum is 22.6h, meaning the top 25% of batteries last between 19.1 and 22.6 hours. Model Y's max is also 22.6, but its Q3 is 19.8, so a smaller percentage of its batteries reach the 20+ mark compared to the spread of X's top quartile.
Analysis B: Model Y has a smaller IQR (~3.5 hours) compared to Model X (~6.3 hours). Model Y is the more reliable choice for predictable performance.
Case Study 2: Morning Rush
1. Range: Expressway: 42 min (52.5-10.5). Main St: 24.5 min (38.5-14). The Expressway has a much larger range and is more likely to have a very long unexpected delay.
2. Skewness: Expressway is Right Skewed (the right whisker/box is much longer than the left). This means while the median is low, there is a long "tail" of potentially very slow commutes.
3. Expert Challenge: Main Street is recommended for reliability. Since 50% of its commutes are faster than the Expressway's 75th percentile, Main St offers a "guaranteed" arrival time that the Expressway cannot match due to its high variability.
3. Box Plot Exit Ticket
Question 1: Which statement is correct?
Set B has a more consistent IQR (smaller box).
Note: Set A's median (16) is significantly lower than Set B's median (65).
Question 2: Skewness
Set B is Left Skewed (the median is closer to the Q3/Max end, and the left whisker is longer). This indicates more values are concentrated at the higher end of the scale.
Question 3: Range
Set A has a wider Range (~70 vs Set B's ~60). Range matters because it shows the total spread and the presence of extreme potential outliers or variation.
Whisker Lesson Plan Teacher Guide Reading the Whiskers
Interpreting & Comparing Box Plots
Lesson Plan
Grade 9 • Algebra 1
Duration
65 Minutes
Objective
Interpret and compare two or more box plots to draw conclusions about data sets.
Materials
Slide Deck
Comparing Test Scores Activity
Box Plot Analysis Worksheet
Exit Ticket
Key Concepts
Interquartile Range (IQR) Skewness & Symmetry Data Consistency Comparative Analysis
Instructional Arc
10
Introduction & Hook: The Scoring Duel
Display two box plots showing points scored per game by two players.
Discussion: "If you had to pick one player for a high-stakes championship game, who would you choose? Why?"Focus on consistency vs. potential .
15
Direct Instruction: Beyond the Five Numbers
Use the Slide Deck to interpret meaning.
Interpreting IQR: 50% of the data lives in the "box." Wider box = more variation.Skewness: Visually identify left, right, and symmetric shapes.The "25% Rule": Every section is exactly 25% of the data.
15
Guided Practice: Comparing Test Scores
Distribute the activity sheet.
Students work in pairs to compare Class A and Class B.
Check: "Which class was more consistent?" and "Is it possible for Class A to have a lower median but highest individual score?"
20
Independent Practice: Analysis Lab
Students complete the lab worksheet.
Scenarios: commute times and battery life.
Focus on writing data-driven comparisons.
05
Wrap-up & Assessment: Exit Ticket
A quick check on comparing medians, IQR, and skewness.
Teacher Tips
Watch For:
Students thinking long whiskers = more data. Remind them: 25% is 25%, no matter the size.
Vocabulary:
Encourage words like 'consistent', 'variable', 'spread', and 'typical value' in their explanations.
Reading the Whiskers Slide Deck Presentation Reading the Whiskers
Interpreting & Comparing Box Plots
Algebra 1 • Data Analysis Lab
Today's Mission
We will interpret and compare multiple box plots to draw conclusions about real-world data.
The Scoring Duel
Player A
Player B
01020304050
Who is the most consistent player?
The 25% Rule
Regardless of size, every section contains 25% of the data points.
1 Lower Whisker
2 Left half of Box
3 Right half of Box
4 Upper Whisker
25%
25%
25%
25%
"Wide sections = Spread out data. Narrow sections = Clustered data."
Measuring Spread
Range
Full spread of all data.
MAX - MIN
Interquartile Range (IQR)
Spread of the "typical" middle 50%.
Q3 - Q1
Smaller IQR = Better Consistency
Skewness & Shape
Symmetric
Right Skewed
Left Skewed
"The skew is the direction of the longer whisker."
Comparing Test Scores Activity Sheet Comparing Test Scores
Guided Practice • Data Analysis Lab
Name:
Date:
Investigating Performance
Two Geometry classes took the same test. Use the box plots below to analyze their performance. Note that Class A has the single highest score in the entire grade.
50%
60%
70%
80%
90%
100%
Class A
Class B
1. 5-Number Summary (Class B)
Min:
Q1:
Med:
Q3:
Max:
2. Interquartile Range (IQR)
Formula: Q3 - Q1
Class A:
Class B:
Which is more consistent?
3. Typical Performance
Compare the medians. Which class has the higher typical score? Justify with data.
4. Consistency Observation
Class B's entire "box" (middle 50%) is located higher than Class A's median. What does this suggest about the majority of students in Class B compared to Class A?
5. Final Judgment
Identify one advantage of Class A's distribution and one advantage of Class B's distribution.
Box Plot Analysis Lab Worksheet Box Plot Analysis Lab
Independent Practice • Applied Data Science
Agent:
01
Case Study: Battery Endurance
Model X
Model Y
10h12h14h16h18h20h22h24h
Analysis A: High Performance
Which model is more likely to give you 20+ hours of battery life? Justify using quartiles.
Analysis B: Predicting Reliability
If consistency is the #1 priority, which model has the smaller Interquartile Range (IQR)? Show your calculation or estimation.
02
Case Study: Morning Rush
Expressway
Main St
0m10m20m30m40m50m60m70m
1. Safer Commute
Identify the Range for both routes. Which route is most likely to have a very long, unexpected delay?
2. Shape of Data
One of these routes is significantly Right Skewed . Which one? What does this mean for the drivers?
3. The Expert Challenge
The Expressway has a faster median time than Main Street. However, at least 50% of the commutes on Main Street are faster than the 75th percentile of the Expressway. Does this change which route you'd recommend?
Box Plot Exit Ticket Exit Ticket
Reading the Whiskers
Name:
1
Compare these two distributions. Which statement is correct?
Set A
Set B
020406080100
Set A has a higher median than Set B.
Set B has a more consistent IQR (smaller box).
At least 50% of Set B is greater than any value in Set A.
2
Is Set B symmetric, right-skewed, or left-skewed? Explain how you know.
3
Which set has a wider Range ? Why does Range matter when analyzing data?
