Lesson 4: Standard Deviation

Review:

• Measures of Center and Boxplots
  • Mean, Median
  • Five-number summary: Min, Q1, Median, Q3, Max
  • Boxplots for comparison

Presentation:

• Demonstrate calculation
  • Calculate the standard deviation for a simple data set: 2 4 6 8 10
  • Video – Standard Deviation
  • Demonstrate using Sleep data

Activity:

Problem 1. During the 2026 FIFA World Cup, the U.S. Men’s National Team scored 11 goals in 5 matches and reached the Round of 16. The team scored 4 goals vs Paraguay, 2 goals vs Australia, 2 goals vs Türkiye, 2 goals vs Bosnia & Herzegovina, and 1 goal vs Belgium.

a. Calculate the mean and standard deviation of goals scored per match.

Problem 2. Six 9th-grade students and six 12th-grade students were asked: how many movies have you seen this month? See their responses below. Which is more spread out, the 9th-grade or 12th-grade data?
9th-grade: 5, 1, 2, 5, 3, 8
12th-grade: 4, 2, 0, 2, 3, 1

a. Calculate the mean and standard deviation for both student groups.
b. Which is more spread out, the 9th-grade or 12th-grade data? Explain using the standard deviations.

Problem 3. Two coffee shops recorded the number of customers who entered during the same six one-hour periods.

Coffee Shop A: 42, 45, 47, 44, 46, 46
Coffee Shop B: 31, 40, 44, 48, 51, 56

a. Calculate the mean and standard deviation for each coffee shop.
b. Which coffee shop has the more consistent number of customers? Explain using the standard deviations.

Lesson 3: Measures of Center and Boxplots

Review:

• Visualizing the shape of the distribution
• Dotplots
• Stemplots
• Histograms
  • Video (00:50-07:00)
  • Demonstrate spreadsheet histogram construction with UN health and economy data (Sheets)

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 using ∑x/n
  • Median
    • Center value within ordered sequence of values
    • Use (n+1)/2 to find the position
    • If $n$ is even: average the two middle values
  • Demonstrate Mean and Median using sleep, work and/or height data
  • Video: Measures of Center (00:50-08:00)
  • Activity:
    • Use the MPG data for Ford vehicles
      • Calculate the mean
      • Find the median
    • Use the MPG data for Honda vehicles
      • Calculate the mean
      • Find the median
        

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• Boxplots
  • Five-number summary
    • Minimum value
    • Quartile 1 (Q1)
    • Quartile 2 (Q2) = Median
    • Quartile 3 (Q3)
    • Maximum value
  • Demonstrate Boxplot construction with sleep, work and height data
  • Video: Boxplots (00:50-08:15)
  • Activity:
    • Use the MPG data for Ford vehicles
      • Find the 5-number summary
      • Make a boxplot
    • Use the MPG data for Honda vehicles
      • Find the 5-number summary
      • Make a boxplot
    • Combine on one axis for comparison
      • Make a single horizontal axis to be shared by both Ford and Honda
      • Add both boxplots to the shared axis to facilitate comparison
      • What do the boxplots suggest about the typical MPG and variability of Ford versus Honda vehicles?

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Exercises:

Problem 1.

Here are the starting salaries, in thousands of dollars, offered to 23 students who earned bachelor’s degrees in computer science.
63 56 66 77 50 53 78 55 90 65 64 69 59 76 48 54 49 68 51 50 70 69 71
a. Make a stemplot.
b. Calculate the mean.
c. Find the five-number summary.
d. Make a boxplot.

Problem 2.

A consumer testing lab measured calories per hot dog in 19 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
a. Make a stemplot.
b. Calculate the mean.
c. Find the five-number summary.
d. Make a boxplot.

Problem 3.

A group of 21 recent college graduates reported the number of minutes they commute to work each morning. Here are the results: 18 24 31 27 22 35 16 29 41 25 20 33 28 19 37 23 26 30 21 34 25

a. Make a stemplot.
b. Calculate the mean.
c. Find the five-number summary.
d. Make a boxplot.

Problem 4.

A sample of 20 grocery stores recorded the price of a particular brand of coffee. Here are the results: 4.90 5.40 6.10 6.80 5.60 7.30 6.50 5.90 5.10 6.90 7.50 5.70 6.30 4.60 7.00 5.80 6.60 5.20 7.40 6.10. Use the Key: 5 | 4 = $5.40.

a. Make a stemplot.
b. Calculate the mean.
c. Find the five-number summary.
d. Make a boxplot.

Lesson 1: Introduction to Advanced Statistics

Presentation:

• Attendance
• Course Overview
  • Syllabus (pdf)
  • Bookmark this course page
  • Blackboard (Bb) – grades only
  • Tutoring
• Computing
  • bring a laptop to class (and be sure it’s charged before class)
  • Google Sheets and Microsoft Excel
  • Excel Essentials in DataCamp

Activity:

• Login to DataCamp
• Begin the Introduction to Excel course
• Confirm successful login and classroom membership (so you aren’t asked to pay for DataCamp) before leaving class today
• Data Camp Tips
  • Refresh frequently during exercises.
  • If using a personal email, send the email address to me so I can send an official invite.
  • Be sure to complete all sections within each Assignment for full credit (otherwise, it will be incomplete)
  • Use hints but not too many. XP will be part of your grade.

Lesson 2: Data Distributions with Stemplots and Dotplots

Review:

• Attendance
• Intro to Statistics
• Syllabus questions
• Watch What is Statistics

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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 or Left Skewed): A distribution with a longer tail on the right or left.
    • Bimodal Distribution: A distribution with two distinct peaks, showing two different groups within the data.
  • 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

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• Dotplots
  • Demonstrate dotplot construction using sleep hours
  • Rules for making dotplots
    • Keep rows and columns neatly aligned
    • Clearly label horizontal axis and vertical axis
    • Try to make each “dot” (circle) the same size

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• Stemplots (aka Stem and Leaf plots)
  • Against All Odds Video – Unit 2 (06:00-11:00) – setup military uniform example
  • Demonstrate stemplot construction using student height and/or hours worked data
  • Rules for making stemplots
    • Keep rows and columns neatly aligned
    • Don’t use commas, decimals or other visible separators
    • Display gaps in data with empty space

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Activity:

• Download the Lesson 2 activity worksheet and complete
• Add this activity to your portfolio

Lesson 1: Intro to Statistics

Presentation:

• Attendance
• Why Statistics?
  • Watch Statistics more useful than Calculus (3 min)
• 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
    • Make-up policy
  • Grading
    • Classroom activities
    • Exams
    • Scores posted on Bb
  • Textbook (optional): Link to Used Textbook on Amazon
  • Mostly pencil/paper, occasional spreadsheet work
• Tips for success in this class
  • Attend class!
  • Engage with in-class activities and exercises
  • Maintain a portfolio of in-class exercises

Activity:

• Watch What is Statistics v2
• Survey handout
• How is Statistics Related to AI?
  • Google or ask an AI: “How are statistics and AI related?”
  • After reading the search results, how would you characterize the relationship between statistics and AI?
    • Unrelated
    • Loosely related
    • Closely related
    • Inseparable
  • How would you explain your choice?

Assignment:

• Be certain you can attend class on at least 4 of the 5 exam dates.