Ch 2 - Frequency Distributions - Student

Frequency Distributions: Chapter 2 Overview

• Definition: A frequency distribution is an organized display of how many individuals are in each score or category derived from a measure.

• Importance: Helps in understanding data patterns and statistical procedures.

Stanford Marshmallow Experiment on Deferred Gratification (Page 2)

• Purpose: Explore how long children can wait for a preferred snack.

• Population: All children.

• Sample: 30 children.

• Construct of Interest: Deferred gratification.

• Operationalization: Measured in minutes waited before eating the snack.

• Variable Type: Continuous.

• Scale Type: Ratio.

Summation Review (Pages 4-5)

• Given Data: 3, 1, 7, 4.

• Calculations:

  • ΣX = 3 + 1 + 7 + 4 = 15.

  • (ΣX)² = 15² = 225.

  • ΣX² = 3² + 1² + 7² + 4² = 9 + 1 + 49 + 16 = 75.

Frequency Distribution Basics (Pages 6-10)

• What is Frequency?: The number of times a score occurs.

• What is Distribution?: Arrangement or spread of scores.

• Uses: To organize data visually (either table or graph).

• Types of Statistics: Descriptive versus inferential.

Frequency Distribution Formats (Pages 11-12)

• Two Main Types:

  1. Tables: Lists each score (X) and the corresponding frequency (f).

  2. Graphs: Visual representations, such as bar graphs and histograms, to depict data.

• Common Data Example: Given table use, with scores ranging between 10 to 18.

Creating a Frequency Distribution Table (Pages 13-28)

• Steps:

  1. Identify the largest value in the dataset.

  2. Count occurrences of each score and record the frequency.

  3. Include all values, even if they do not occur, from the smallest to the largest.

  4. Double-check the total frequency against the dataset size.

Proportion and Percentage Calculations (Pages 31-38)

• Proportion Formula: f/N, where f = frequency and N = total number of scores.

• Percentage Calculation: Proportion x 100.

• Example Calculation:

  • For score 18, f = 1 → Proportion = 1/20 = 0.05 → Percentage = 5%.

Grouped Frequency Distribution Table (Pages 43-50)

• Purpose: To manage large datasets visually.

• Guidelines:

  • Should contain about 10 class intervals.

  • All intervals should have equal width.

  • Simplify interval width selections (usually multiples of 2, 5, or 10).

Graphing Frequency Distributions (Pages 78-110)

• Types of Graphs:

  • Bar Graphs: For nominal/ordinal data; gaps between bars.

  • Histograms: For interval/ratio data; no gaps, with heights indicating frequency.

• Polygons: Dots above scores connected to show frequency distribution.

• Characteristics:

  • Symmetrical vs. skewed distributions.

  • Tail direction indicates positive (right) or negative (left) skew.

Homework Review (Pages 119)

• Assignments: Follow-up on chapters and frequency distributions, including constructing frequency tables and practicing calculations.