Lesson 2: Data Distributions with Stemplots and Histograms

August 28, 2025

Review:

• Attendance
• Intro to Statistics
• Syllabus
• Textbook

Presentation:

• Data Distributions
  • The “shape” of the data
  • Distribution of “Factfulness” survey scores
  • Distribution of Exam Scores
  • Types of common distributions
    • Normal Distribution: A symmetric bell-shaped curve, where most data points cluster around the mean.
    • Uniform Distribution: A flat distribution, where all outcomes are equally likely.
    • Skewed Distribution (Right Skewed): A distribution with a longer tail on the right, indicating a few high values.
    • Bimodal Distribution: A distribution with two distinct peaks, showing two different groups within the data.
    • Exponential Distribution: A distribution with a rapid decline, often used to model time between events.
    • Poisson Distribution: A distribution that models the number of events occurring within a fixed interval of time.
    • Binomial Distribution: The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It’s widely used in scenarios where there are only two possible outcomes, often labeled as “success” and “failure.”
  • Visualize the distribution of data you want to understand
    • Picture is worth a thousand words
    • Not much training necessary to look at a data graphic
    • Improved approach for detecting “patterns” and inviting “participation“
    • Use stemplots for small datasets
    • Use histograms for large datasets
• Stemplots (aka Stem and Leaf plots)
  • Against All Odds Video – Unit 2
  • Demonstrate stemplot construction
    • Female heights (cm): 152, 157, 160, 165, 165, 168, 170, 170, 170, 173, 173, 180
    • Stemplot Rules
      • Keep rows and columns neatly aligned
      • Don’t use commas, decimals or other visible separators
      • Display gaps in data with empty space
  • Activity: Using the vehicle mpg data (see below), create three stemplots
    • Top Selling Midsize Cars in the US
    • Top Selling Midsize Cars in Europe
    • Back to back comparison – US vs Europe
• Histograms
  • Against All Odds Video – Unit 3
  • Demonstrate spreadsheet histogram construction
    • Student Height Data (Sheets)
    • UN health and economy (Sheets)
  • Activity: Using the same vehicle mpg data (below), create two histograms
    • Top Selling Midsize Cars in the US
    • Top Selling Midsize Cars in Europe
    • Use Google Sheets or Microsoft Excel

Assignment:

• Read Lesson 02
• Create a frequency distribution to help decipher this encrypted quote from a key 20th Century figure.
• “LKVNYFMJQ MA FPL WJAF EJBLXDVR BLYEJQ BPMNP SJV NYQ VAL FJ NPYQHL FPL BJXRK.”
• – QLRAJQ WYQKLRY

Activity Data:

Top Selling Midsize Cars in the US – MPG

• Toyota Camry – 32
• Honda Accord – 33
• Nissan Altima – 30
• Subaru Outback – 29
• Ford Fusion – 27
• Chevy Malibu – 26
• Kia Optima – 27
• Volkswagen Passat – 29
• Subaru Legacy – 29
• Hyundai Sonata – 30

Top Selling Midsize Cars in the Europe – MPG

• Volkswagen Passat – 35
• Skoda Superb – 66
• Opex Insignia – 53
• Ford Mondeo – 48
• Renault Talisman – 35
• Toyota Avensis – 63
• Mazda 6 – 30
• Peugeot 508 – 62
• Kia Optima – 58
• Hyundai i40 – 67