Lesson 4: Measuring Variance and Standard Deviation

September 4, 2025

Review:

• Quiz
• Measures of Center and Boxplots
  • Mean, Median, Percentiles, Quartiles
  • Five-number summary
  • Min, Q1, Median, Q3, Max
  • Quartiles and Boxplots (U. Illinois)
  • Boxplot Grapher: http://www.imathas.com/stattools/boxplot.html

Presentation:

• Demonstrate calculation
  • Calculate the standard deviation for a simple data set: 2, 4, 6, 8, 10
  • Against All Odds – Video Unit 6
  • Calculate the standard deviation for the following (n=10) exam scores:
    • 80 73 92 85 75 98 93 55 80 90
    • Demonstrate by hand
    • Demonstrate in Google Sheets

Activity:

Problem 1. Below are the number of home runs that Babe Ruth hit in each of his 15 years with the New York Yankees, 1920 – 1934. Calculate the mean and standard deviation.
54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 

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. Calculate the mean and standard deviation for each data set. 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

Assignment:

Repeat Problems 1 and 2 (above) using Sheets