Statistics

Attendance Tracking

  • Attendance will no longer be called out; instead, there will be a sign-in sheet for students to initial.

  • Students are asked to pass the sheet around after signing.

Course Outline and Homework

  • The discussion begins on January 29, focusing on Module Two.

  • First homework assignment is due on Sunday by midnight, covering Module One materials.

  • Homework can be found embedded in Module One on Canvas.

Frequency Distributions

Learning Objectives

  • Understand how to construct a frequency distribution.

  • Discuss different shapes of distributions.

  • Familiarize with graphing techniques for qualitative and quantitative variables (Refer to Chapter Two of the textbook for this).

Definition

  • Frequency Distribution: An organized tabulation of the number of individuals located in each category on a scale of measurement.

  • This is an account of how many times a particular score appears within each category of measurement.

Examples and Explanation

  • Consider a dataset of 16 scores ranging from 1 to 7.

  • A frequency distribution organizes this information in a table, counting instances of each score.

  • Example of a frequency distribution table layout:

    • Column x: Represents the different scores (1 through 7).

    • Column f (frequency): Number of times each score appears in the data set.

    • Layout:

    • x | f

    • 1 | 3

    • 2 | 1

    • 3 | 4

    • 4 | 2

    • 5 | 2

    • 6 | 2

    • 7 | 1

Description of Columns

  • Column x: Different values of scores in the data set.

  • Column f: The count of each score.

  • Example:

    • x = 1 has frequency 3, meaning the score 1 appears three times in the dataset.

Cumulative Frequency

  • Cumulative Frequency: The number of scores that fall at or below a given value of x.

  • Constructed by starting from the smallest value of x and working towards the largest.

  • Cumulative frequency table example:

    • Column cf: Cumulative frequencies based on previous frequencies.

    • Layout:

    • x | f | cf

    • 1 | 3 | 3

    • 2 | 1 | 4

    • 3 | 4 | 7

    • 4 | 2 | 9

    • 5 | 2 | 11

    • 6 | 2 | 13

    • 7 | 1 | 16

  • The last cumulative frequency should equal the total number of scores in the set (16).

Proportions

  • Proportions: The share of scores that have a given value of x relative to the total number of scores.

  • Calculated as the frequency for each value of x divided by the sum of the frequencies (total number of scores).

    • Example: For x = 1, if frequency is 3 and total scores are 16, then proportion = \frac{3}{16} = 0.19.

  • Rounding is to the nearest hundredth.

Cumulative Proportions

  • Cumulative Proportions: Proportion of scores that fall at or below a given value of x.

  • Calculated as cumulative frequency divided by the total number of scores:

    • Example for x = 1: \frac{cf_{x=1}}{\text{sum of f}} = \frac{3}{16} = 0.19.

  • Cumulative proportions for highest value in the set will always equal 1 (e.g., for x = 7).

Group Activity

  • Students will work in small groups to practice constructing frequency distributions.

  • Each group will fill in columns for x, f, cf, p, and cp based on a provided set of scores.

Key Takeaways

  • There are multiple ways to check the accuracy of the cumulative frequency, proportions, and cumulative proportions.

  • Constructing and reviewing frequency distributions aids in visualizing datasets.

  • It's important to start with the lowest value of x when constructing cumulative frequencies and proportions.

  • Signs of confusion during group work indicate areas needing further clarification from the instructor.