Class width is a fundamental concept in statistics used when organizing data into frequency distributions. It represents the size or range of each class interval when dividing a dataset into groups. Properly determining class width is essential for creating meaningful and interpretable frequency distributions, histograms, and other statistical visualizations.
Class width (also called class size or class interval) refers to the numerical difference between the upper and lower boundaries of a class in a grouped frequency distribution. It determines how broad each category will be when organizing data points into discrete groups or "bins."
When data is organized into a frequency distribution, the entire range of values is divided into a series of non-overlapping intervals of equal width. The class width determines the size of these intervals.
The formula for calculating class width is:
Class width = (Maximum value - Minimum value) / Number of classes
Where:
This formula ensures that all classes have equal width and that the entire range of data is covered from the minimum to the maximum value.
Selecting an appropriate class width is crucial for creating informative frequency distributions:
Too small: If the class width is too small, you'll have too many classes, making the distribution difficult to interpret and potentially obscuring patterns in the data.
Too large: If the class width is too large, you'll have too few classes, potentially losing important details and variations in the data.
The goal is to choose a class width that reveals the underlying structure of the data without introducing unnecessary complexity or oversimplification.
Dataset range: 23 to 79 Number of classes: 7
Class width = (79 - 23) / 7
= 56 / 7
= 8
test
The class intervals would be: 23-31, 31-39, 39-47, 47-55, 55-63, 63-71, 71-79
A teacher collected test scores ranging from 45 to 98 and wants to create a frequency distribution with 6 classes.
Class width = (98 - 45) / 6
= 53 / 6
≈ 8.83
Since class width typically needs to be a convenient number, the teacher might round up to 9. The class intervals would be: 45-54, 54-63, 63-72, 72-81, 81-90, 90-99
When determining class width in practice, consider these guidelines:
Round to convenient numbers: Class widths are often rounded to convenient numbers (5, 10, 25, etc.) for easier interpretation.
Adjust the minimum and maximum: You might need to adjust the minimum and maximum values slightly to accommodate a convenient class width.
Equal class widths: In most cases, all classes should have the same width for proper comparison.
Number of classes: Statisticians often recommend between 5-20 classes, depending on the sample size. Common rules include Sturges' rule or the square root rule.
Open-ended classes: For extremely skewed data, you might use open-ended classes at one or both extremes (e.g., "less than 20" or "greater than 100").
Understanding class width is essential for: