In a frequency distribution, a class interval represents the difference between the upper class limit and the lower class limit.
In other words, a class interval represents the width of each class in a frequency distribution.
Class intervals can be presented in two common scenarios:
1. When class limits are already defined: In this case, you simply calculate the difference between the upper and lower limits of each class.
2. When working with raw data: When you have only raw data points (e.g., 20, 56, 40, 70) without predefined classes, you’ll need to first establish appropriate class limits before calculating intervals.
For raw data, determining class intervals involves these steps:
- Calculate the range of your data (maximum value minus minimum value)
- Decide on an appropriate number of classes (typically 5-15, depending on your data size)
- Divide the range by your chosen number of classes to find an approximate class width
- Round to a convenient number for easier interpretation
- Create your classes starting from or just below your minimum value
Once you’ve established your classes, the class interval is consistent across all classes in a well-designed frequency distribution.
The following examples show how to calculate class intervals for different frequency distributions, starting with cases where class limits are already defined.
Example 1: Calculating Class Intervals
Suppose we have the following frequency distribution that represents the number of wins by different basketball teams:
The lower class limit and upper class limit are simply the smallest and largest possible values in each class:
The class interval is the difference between the upper class limit and the lower class limit.
For example, the size of the class interval for the first class is 30 – 26 = 4.
Similarly, the size of the class interval for the second class is 31 – 35 = 4.
If we calculate the size of the class interval for each class in the frequency distribution, we’ll find that each class interval has a size of 4.
Example 2: Calculating Class Intervals
Suppose we have the following frequency distribution that represents the exam grades received by students in a certain class:
The lower class limit and upper class limit are simply the smallest and largest possible values in each class:
The class interval is the difference between the upper class limit and the lower class limit.
For example, the size of the class interval for the first class is 30 – 21 = 9.
Similarly, the size of the class interval for the second class is 40 – 31 = 9.
If we calculate the size of the class interval for each class in the frequency distribution, we’ll find that each class interval has a size of 9.
Example 3: Using the Square Root Method
The square root method is a common approach to determine the appropriate number of classes when working with raw data.
Suppose we have collected the following 25 data points representing the ages of participants in a study:
18, 19, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 40, 42, 45, 48, 52, 55, 58, 62, 65
Step 1: Determine the number of classes using the square root of the total number of observations.
Number of classes = √25 = 5
Step 2: Find the range of the data.
Range = Maximum value – Minimum value = 65 – 18 = 47
Step 3: Calculate the class interval.
Class interval = Range ÷ Number of classes = 47 ÷ 5 = 9.4 ≈ 10
Step 4: Create the frequency distribution with class interval of 10.
| Class Limits | Frequency |
|---|---|
| 18 – 27 | 7 |
| 28 – 37 | 8 |
| 38 – 47 | 4 |
| 48 – 57 | 3 |
| 58 – 67 | 3 |
In this example, using the square root method, we determined a class interval of 10, which resulted in a well-balanced frequency distribution.
Example 4: Using Sturges’ Rule for Class Intervals
Sturges’ Rule is a more sophisticated formula for determining the number of classes.
Suppose we have the following 40 data points representing the scores on a standardized test:
62, 65, 67, 69, 70, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 90, 91, 92, 92, 93, 94, 95, 96, 97, 98, 99
Step 1: Apply Sturges’ Rule to determine the number of classes.
Number of classes = 1 + 3.322 × log₁₀(number of observations)
Number of classes = 1 + 3.322 × log₁₀(40)
Number of classes = 1 + 3.322 × 1.602
Number of classes = 1 + 5.322 = 6.322 ≈ 6
Step 2: Find the range of the data.
Range = Maximum value – Minimum value = 99 – 62 = 37
Step 3: Calculate the class interval.
Class interval = Range ÷ Number of classes = 37 ÷ 6 = 6.17 ≈ 6
Step 4: Create the frequency distribution with class interval of 6.
| Class Limits | Frequency |
|---|---|
| 62 – 67 | 3 |
| 68 – 73 | 4 |
| 74 – 79 | 5 |
| 80 – 85 | 10 |
| 86 – 91 | 9 |
| 92 – 97 | 7 |
| 98 – 103 | 2 |
Note: We created 7 classes instead of 6 to accommodate all data points.
Sturges’ Rule provides a scientific approach to determining an appropriate number of classes based on the sample size, which results in a class interval that effectively displays the distribution of the data.
Wrapping Up
Finding appropriate class intervals is an important step in creating effective frequency distributions. When class limits are already defined, calculating the interval is straightforward. When working with raw data, methods like the range approach, square root method, or Sturges’ Rule can help determine suitable intervals.
Well-chosen class intervals allow you to organize data in a way that reveals patterns and makes statistical analysis more manageable. The goal is to create classes that are neither too wide (hiding important details) nor too narrow (creating too many classes with few observations).
Additional Resources
How to Find Class Boundaries
How to Find Class Limits
How to Find Class Midpoints
What if the class interval is not giving, how do you determine the it, example: 20, 56, 40, 70, etc. How can you determine the upper and lower class limit.
Thank you for your great question, Olisa!
I’ve actually updated the introduction section of this post to address exactly this scenario.
In short, when you have raw data like 20, 56, 40, 70, you’ll need to:
1. Find the range (highest minus lowest value)
2. Choose a number of classes (usually 5-15)
3. Calculate approximate class width: Range ÷ Number of classes
4. Create your classes, starting near your minimum value
Please check the updated introduction for a detailed explanation of this process. I appreciate you bringing up this important point that many students encounter!
How can we know that a question can be or cannot be divided into ckass interval
Hi Farhaan:
Any quantitative data can be organized into class intervals. If your data consists of numerical values with a meaningful range (like test scores, ages, weights, etc.), it can be divided into class intervals. The only limitation would be categorical data (like names, colors, or types) which cannot be meaningfully grouped into numerical ranges.
This really ease my understanding. Thank you.
I have a data where there were no upper and lower class limit l, but it says I should construct an appropriate distribution table, hence class interval must be necessary how do you think I go about it
Thank you 🙏🏻
Hi Victory:
For data without predefined class limits, follow the steps in our updated introduction: Calculate the range of your data, decide on an appropriate number of classes (5-15), divide the range by this number to find the class width, round to a convenient number, and create your classes starting from your minimum value. Examples 3 and 4 in the post demonstrate this process using different methods.
How do we find the class interval in a frequency table that has classes with different class intervals?
Hi Babaga Grace:
When a frequency table has classes with different intervals, each class interval must be calculated separately. You simply take the difference between the upper and lower limit for each individual class. This variation in intervals isn’t ideal for statistical analysis, but you can calculate and report each interval as is. For better analysis, consider reorganizing the data with consistent intervals if possible.
I didn’t understand that part of frequency, where did you obtain those figures in frequency line
Hi Oliha Juma:
The frequency values represent the count of data points that fall within each class. For instance, in Example 1, the frequency “5” in the first row means that 5 basketball teams had between 26-30 wins. These numbers come from counting the original data points that fall into each range. In practice, you’d count how many data values fall within each class interval.
I don’t understand the explanation
Hello…Please clarify what parts you would like explained further.
Hi Atolagbe Anthony Temitope:
I’d be happy to clarify specific parts that are confusing. The basic concept is that class intervals are the width or “span” of each group in your data. For example, in a class of “20-29,” the interval is 10 (29-20+1). Which particular aspect of the explanation would you like me to elaborate on?