StatPsy - Prelims Part 2.pptx
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
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
Scores | Tally | Frequency | Percent |
|---|---|---|---|
70-79 | 5 | 5 | 16.67% |
60-69 | 6 | 6 | 20.00% |
50-59 | 9 | 9 | 30.00% |
40-49 | 4 | 4 | 13.33% |
30-39 | 6 | 6 | 20.00% |
Total | 30 | 100.00% |
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
Age | Tally | Frequency | Percent |
|---|---|---|---|
23 | 6 | 6 | 13.33% |
22 | 6 | 6 | 13.33% |
21 | 0 | 0 | 0.00% |
20 | 7 | 7 | 15.56% |
19 | 6 | 6 | 13.33% |
18 | 7 | 7 | 15.56% |
17 | 5 | 5 | 11.11% |
16 | 8 | 8 | 17.78% |
Total | 45 | 100.00% |
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.