Page 1: Introduction

Psychological Statistics

• Course by JADE G. VILLANUEVA, CSPE, RPM

• Lecturer

Page 2: Frequency Distribution

Definition

• A frequency distribution quantifies the number of observations for each possible value of a variable.

• Depicted using graphs and frequency tables.

Page 3: Definition of Terms

Key Concepts

• Variable: An attribute of an object of study.

• Frequency: The number of times a value occurs in a dataset.

• Cumulative Frequency: Sum of a frequency and all preceding frequencies.

Page 4: Types of Frequency Distribution

Categories

• Ungrouped Frequency Distributions: Lists frequencies of individual data values.

• Grouped Frequency Distributions: Organizes data into groups (class intervals) with corresponding frequencies.

Page 5: Example of Grouped Frequency Distribution

Given Scores

• Scores from a class of 30 students: 48, 73, 57, 50, ... (complete list omitted for brevity)

Page 6: Step 1 – Determine Range

Steps to Analyze

1. Identify highest and lowest score.

   • Highest Score: 79

   • Lowest Score: 30

   • Range: 49

Page 7: Step 2 – Variation of Scores

Calculation

• Use 5 as the number of intervals.

• Interval Calculation: Range (49) ÷ Number of Steps (5) = 9.8 → Round to 10.

Page 8: Step 3 – Lower Limit

Setup for Grouping

• Use the lowest score (30) as the lower limit for the first interval.

Page 9: Step 4 – Adding Intervals

Continuation

• Add calculated interval (10) to lower limit (30) to get 40.

• Repeat to complete group distribution.

Page 10: Step 5 – Counting Frequencies

Final Steps

• Count matching scores for each interval.

• Frequency represents tallies; calculate percentage of total.

Page 11: Grouped Frequency Distribution Table

Scores Summary

Page 12: Example of Ungrouped Frequency Distribution

Given Ages

• Ages of 45 students: 17, 18, 16, ... (complete list omitted for brevity)

Page 13: Step 1 – Count Occurrences

Process

• Tally the occurrences for each age to find frequency; calculate percentage.

Page 14: Ungrouped Frequency Distribution Table

Age Summary

Page 15: Graphical Presentation

Overview

• Data can be visually presented through various formats:

  • Pie chart

  • Histogram or bar graph

  • Frequency polygon or line graph

Page 16: Pie Chart

Characteristics

• Represents relative frequency distribution of nominal variables.

• Divided circle showing each value's relative frequency.

• Effective for emphasizing frequent/infrequent variables.

• Disadvantage: Hard to compare small differences.

Page 17: Example Pie Chart

2022 Winter Olympics Medals

• Gold: 40%

• Silver: 28%

• Bronze: 32%

Page 18: Bar Chart

Characteristics

• Displays frequency or relative frequency of categorical variables.

• Each value represented by a bar with height indicating frequency.

• Easier to compare frequency across different values than pie charts.

Page 19: Example Bar Chart

Bird Species Frequency

• Graph representing bird species counts at a feeder by frequency.

Page 20: Polygon or Line Chart

Usage

• Histograms show frequency distribution of quantitative variables using plotted points.