Lesson 2: Data Distributions with Stemplots and Histograms

August 22, 2024

Review:

• Attendance
• Intro to Statistics
• Syllabus
• Textbook
• Factfulness survey

Presentation:

• Data Distributions
  • The “shape” of the data
  • 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
• Histograms
  • Against All Odds Video – Unit 3
  • Demonstrate spreadsheet histogram construction
    • Student Height Data (Sheets)
    • UN health and economy (Sheets)

Activity:

• Using the vehicle mpg data (below), create three stemplots
  1. Top Selling Midsize Cars in the US
  2. Top Selling Midsize Cars in Europe
  3. Back to back comparison – US vs Europe
• Using the same vehicle mpg data (below), create two histograms
  1. Top Selling Midsize Cars in the US
  2. Top Selling Midsize Cars in Europe
  3. Use Google Sheets or Microsoft Excel

Study:

• Read Lesson 02

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

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

Bonus Challenge:

Create a frequency distribution to help decipher this encrypted quote from a famous 20th Century leader.

“LKVNYFMJQ MA FPL WJAF EJBLXDVR BLYEJQ BPMNP SJV NYQ VAL FJ NPYQHL FPL BJXRK.”

• QLRAJQ WYQKLRY