1/15/26 venn diagrams

Attendance and Class Reminders

  • The class discussed the attendance and participation process.

  • Important reminders regarding class messaging about resources and study groups.

  • Mention of custom books linked through Blackboard for better assistance.

Class Support and Resources

  • Office hours scheduled for Fridays to assist students.

  • Encouraged students to attend third hours for individual help or study groups.

  • Mention of cheaper textbook options available online.

  • Note: No late penalties currently imposed for submissions this week.

Student Participation

  • Several students had individual challenges (e.g., car issues, health concerns).

  • Understanding from the instructor regarding personal situations impacting attendance.

  • Encouragement to utilize Teams for participating in class if unable to attend physically.

  • Emphasis on accessing resources and support via class announcements.

Course Content Overview

Probability and Statistics Concepts

  • Discussion on creating two-way tables using data on handedness among men and women.

  • Definition: A two-way table displays the frequency distribution of two categorical variables.

  • Example percentages given: 12% of men are left-handed, 9% of women are left-handed.

Two-Way Table Construction

  • Total men: 150, Total women: 200

  • For men:

    • Left-handed = $12 ext{ percent} = 0.12 imes 150 = 18$ (Left-handed men)

    • Right-handed = $100 ext{ percent} - 12 ext{ percent} = 88 ext{ percent}$. Right-handed men = $0.88 imes 150 = 132$

  • For women:

    • Left-handed = $9 ext{ percent} = 0.09 imes 200 = 18$ (Left-handed women)

    • Right-handed = $100 ext{ percent} - 9 ext{ percent} = 91 ext{ percent}$. Right-handed women = $0.91 imes 200 = 182$

  • Totals summarized:

    • Left-handed: $18 + 18 = 36$

    • Right-handed: $132 + 182 = 314$

Graphical Representation

  • Introduction to Venn diagrams using categories of handedness among genders.

  • Highlighting importance of proper graph representation when selecting categories (males, females, handedness).

  • Example: Males versus Left-handed.

  • Key calculations reiterated for clarity on figure manipulation within Venn diagrams.

Venn Diagram Construction

  • Interaction between different groups illustrated through two Venn diagrams comparing two categories.

  • Emphasis on overlap in Venn diagrams and counting methodology to arrive at the correct subset distributions.

  • Address of alternative graph arrangements based on problem requirements.

Additional Problems and Homework Assignments

  • Next problems analyzed involved interpreting a three-circle Venn diagram addressing employment, locality, and educational status at a conference.

  • Important clarifications made about categorizing employed locals versus those without a college degree.

  • Instruction provided for correctly identifying group sizes and ensuring accurate count representation in Venn diagrams.

Practice Problem: Drug Test Results for Runners

  • Example of drug test categorization presented with positive and negative results; necessity for careful counting and number accuracy explained.

  • Problem required filling out a table based on runners' test results and associated representations, emphasizing data integrity between subgroups.

Wrap-Up and Next Classes

  • Students reminded of upcoming class cancellations.

  • Reiteration of third hours available for continued assistance with difficulties in course material and technology (e.g., Pearson access).

  • Instructor's ongoing availability to respond to student emails for supportive measures regarding attendance and participation.