Differentiated 15-Minute Lesson on Interpreting Data Shape, Center & Spread (Including Outliers)

Hi Steve! It's great to work with you again. Handling shape, center, and spread in just 15 minutes is a sprint, but we can definitely make it impactful by using targeted data sets.

Since you have three distinct groups, I’ve designed these "Mini-Lessons" to be high-impact. Each one uses a specific scenario to highlight how outliers "tug" at the data.

To help with your presentation, if you'd like to turn these into visual aids, I recommend using Alayna's AI Slides Generator for Google Slides. You can install it from the Google Workspace Marketplace and access it via Extensions → Alayna AI for Google Slides™.

5-Minute Lesson: The "Outlier Effect"

To help with your presentation, if you'd like to turn these into visual aids, I recommend using Alayna's AI Slides Generator for Google Slides. You can install it from the Google Workspace Marketplace and access it via Extensions -> Alayna AI for Google Slides.

Group 1: The "Building Blocks" Group (Struggling)

Goal: Visually identify outliers and understand that the mean is "sensitive" while the median is "stubborn."

The Scenario: The Pizza Party Imagine 5 friends count how many slices of pizza they ate: 2, 2, 3, 3, 4.

• Center: Mean = 2.8, Median = 3.
• Spread: Range = 2 (from 2 to 4).

The Twist (The Outlier): A competitive eater joins the party and eats 20 slices. The data is now: 2, 2, 3, 3, 4, 20.

Activity (5-7 mins):

1. Calculate the new center:
   • New Mean: (2+2+3+3+4+20) divided by 6 = 5.6
   • New Median: The middle is between 3 and 3, so Median = 3.
2. Discussion:
   • Did the "average" person really eat almost 6 slices? No!
   • The outlier (20) pulled the mean way up, but the median stayed the same.
3. Shape: This data is now "Skewed Right" because the outlier pulled the "tail" toward the high numbers.

Key Takeaway: When you have a "crazy" outlier, use the Median to describe the center because it isn't fooled by extreme points.

Group 2: The "Get It" Group (On-Track)

Goal: Compare two distributions and choose the best measure of center and spread based on shape.

The Scenario: Two Tech Startups

• Company A (Symmetric): Five employees earn 50k, 52k, 50k, 48k, 50k.
• Company B (Skewed): Four employees earn 30k, 35k, 32k, 33k, and the CEO earns 250k.

Activity (5-7 mins):

1. Analyze Shape: Company A is symmetric (balanced). Company B is heavily skewed right due to the CEO’s salary (the outlier).
2. Compare Centers:
   • Company B Mean: Approximately 76,000.
   • Company B Median: 33,000.
3. The Context Question: If you are looking for a job, which number is more "honest" about what you will probably earn?
   • The Mean (76k) makes it look high, but the Median (33k) is what most people actually make.

Key Takeaway: For symmetric data, use the Mean. For skewed data with outliers, use the Median.

Group 3: The "Analysts" Group (Ready to Go Deeper)

Goal: Justify the removal of outliers and understand "Resistance."

The Scenario: The Biology Lab Students are measuring the growth of plants in centimeters: 12, 14, 13, 15, 12, 14, 0, 45.

Activity (5-7 mins):

1. Identify Two Outliers:
   • The 0 (The plant died).
   • The 45 (A possible recording error; maybe it was 4.5 or 45 millimeters).
2. The "Resistance" Test:
   • Mean with outliers: 15.6 cm.
   • Mean without outliers: 13.3 cm.
3. The Challenge: Should we delete these points?
   • If the 0 is a real result (the plant died), we should keep it but use the Median to describe the "typical" plant.
   • If the 45 is a typo, we should remove it because it "breaks" our data.

Key Takeaway: Outliers are not always "bad" data, but they require us to use resistant measures (Median and IQR) that don't change drastically when extreme values are added.

Quick Check for All (Final 2 Minutes)

Ask the whole class: "If a billionaire walks into a room of 10 average people, does the Mean wealth of the room go up? Does the Median wealth change much?"