Table of Contents
What Is a Frequency Distribution?
A frequency distribution organizes raw data by showing how many times each value (or range of values) occurs. It transforms a disorganized list of numbers into a structured table that reveals patterns, central tendency, and spread. Frequency distributions are the foundation for histograms, bar charts, and many statistical analyses.
There are two main types: ungrouped (for discrete data with few unique values) and grouped (for continuous data or data with many unique values, organized into class intervals). Both show frequency (count), relative frequency (proportion), and cumulative frequency.
Types
| Type | Data | Example |
|---|---|---|
| Ungrouped | Discrete, few values | Dice rolls: 1(3), 2(5), 3(4)... |
| Grouped | Continuous, many values | Ages: 0-9(12), 10-19(18)... |
How to Create One
- Sort data from smallest to largest
- Determine number of classes (Sturges' rule: k = 1 + 3.322 log(n))
- Calculate class width = range / number of classes
- Count frequency for each class
- Add relative and cumulative frequencies
Example
For data: 1,2,2,3,3,3,4,4,4,4 the ungrouped frequency distribution is: 1 appears 1 time (10%), 2 appears 2 times (20%), 3 appears 3 times (30%), 4 appears 4 times (40%). The mode is 4 with the highest frequency.
Frequently Asked Questions
How many classes should I use?
Sturges' rule suggests k = 1 + 3.322 × log10(n). For n=100, that is about 8 classes. More classes reveal more detail but may obscure patterns. 5-15 classes is typically appropriate.
What is relative frequency?
Relative frequency = class frequency / total count. It represents the proportion (or percentage) of data in each class. All relative frequencies sum to 1 (or 100%).
What is cumulative frequency used for?
Cumulative frequency shows running totals, useful for finding percentiles and drawing ogives (cumulative frequency curves). The last cumulative frequency always equals the total count.