Lesson 3: Measures of Center, Percentiles and Boxplots

Review:

• Attendance
• Visualizing the shape of the distribution
• Stemplots
• Histograms
  • Against All Odds Video – Unit 3
  • Demonstrate spreadsheet histogram construction
  • Histogram ≠ Column Chart
  • UN health and economy (Sheets)
• Cryptogram with frequency distribution – anyone solve?

Presentation:

• Measures of Center
  • Mean
    • Same as Average
    • Sum of values divided by count, or ∑x/n
    • n = total number of observations/measurements/values
    • Example
  • Median
    • Center value within ordered sequence of values
    • Same as 50th Percentile
    • Position = 0.50*n
      • n = total number of observations
      • round to the nearest whole number
      • alternative for small (n<30) data sets = (n+1)/2
    • Example
  • Video: Measures of Center
• Percentiles and Boxplots
  • Percentiles
  • To find the xth percentile
    • calculate x/100 * n (rounded to the nearest integer or take average of two values on either side)
    • result is the position of the value in an ordered (smallest to largest) data set
    • 25th percentile = 25/100 * n
    • 50th percentile = 50/100 * n = Median
    • 75th percentile = 75/100 * n
    • Example with Female height data
• • Boxplots
  • Five number summary
    • 25th Percentile = Q1
    • 50th Percentile = Q2 = Median
    • 75th Percentile = Q3
    • Minimum value
    • Maximum value
    • Range = Max – Min
    • Interquartile Range (IQR) = Q3 – Q1
    • Example with Male height data
  • Video: Boxplots

Activity:

Problem 1.

Here are the starting salaries, in thousands of dollars, offered to 20 students who earned bachelor’s degrees in computer science in 2011.
63 56 66 77 50 53 78 55 90 65 64 69 59 76 48 54 49 68 51 50
a. Make a stemplot.
b. Find the median, mean and mode.
c. Find the five-number summary.
d. Make a boxplot.
e. Compute the range and interquartile range (IQR).

Problem 2.

A consumer testing lab measured calories per hot dog in 20 brands of beef hot dogs. Here are the results:
186 181 176 149 184 190 158 139 175 148 152 111 141 153 190 157 131 149 135 132
a. Make a stemplot.
b. Find the median, mean and mode.
c. Find the five-number summary.
d. Make a boxplot.
e. Compute the range and interquartile range (IQR).

These problem descriptions (#1 and #2) are from “Against All Odds”, modified slightly and copied here for convenience.

Problem 3.

Use the MPG data for top selling midsize cars in the US and European markets from Lesson 1.

a. Find the five-number summaries.
b. Produce 2 boxplots, one for each market, and put them both on the same chart to facilitate comparison.

Assignment:

• For class on Thu
  • Use the UN health and economy data (filter to display North and South America only).
  • Use Google Sheets (or Excel) to create a histogram for Life Expectancy, Infant Mortality and GDP Per Capita (3 separate histograms)
  • Compute the 5-number summary for Life Expectancy, Infant Mortality and GDP Per Capita (1 5-number summary for each variable).
  • Be prepared to share your histograms and 5-number summaries.

Lesson 2: Data Distributions with Stemplots and Histograms

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

Lesson 1: Introduction to Statistics

Presentation:

• Attendance
• Why Statistics?
  • Watch Statistics more useful than Calculus (3 min)
  • The Data Science and Analytics Revolution (see HBR articles below)
• Statistics is different
  • This won’t be the same old math class.
  • Give me and statistics a chance.
• Course Overview
  • Syllabus (PDF)
  • Bookmark this course page
  • Classroom activities
  • Exams
    • Reviews
    • Format of Midterms vs the Final
    • Make-up policy
  • Grading
    • Assignments/activities
    • Exams
    • Scores posted on Bb
  • Textbook (optional): Link to Used Textbook on Amazon
  • Mostly pen/paper, some spreadsheet work
• Tips for success in this class
  • Attend class!
  • Engage with in-class activities and assignments
  • Attend the review session prior to each exam
  • Study by practicing the problems we work on during class

Activity:

• “Factfulness”
  • Questions
  • Watch The Best Stats You’ve Ever Seen (0:00 – 06:00)

Study:

• Reading for Thu
• Recommended (not required)
  • Introduction to the Practice of Statistics, 6th Edition (textbook on Amazon)
  • Factfulness by Hans Rosling (book on Amazon)
  • Data Scientist: The Sexiest Job of the 21st Century (HBR article)
  • Is Data Scientist Still the Sexiest Job of the 21st Century? (HBR article)