What is the formula to find the class width(or class interval) in the grouped frequency distribution?
The Correct Answer and Explanation is :
The formula to find the class width (or class interval) in a grouped frequency distribution is: Class Width=Upper Limit of a Class−Lower Limit of the Class\text{Class Width} = \text{Upper Limit of a Class} – \text{Lower Limit of the Class}
This can also be calculated by using the following formula: Class Width=Range of DataNumber of Classes\text{Class Width} = \frac{\text{Range of Data}}{\text{Number of Classes}}
Where:
- Range of Data is the difference between the maximum and minimum values of the data set.
- Number of Classes refers to the total number of classes or intervals you want to divide the data into.
Explanation:
In a grouped frequency distribution, data is organized into classes (or intervals) to represent a range of values. To maintain consistency in the distribution and ensure that each class has a uniform width, the class width is calculated. The purpose of calculating class width is to define the intervals in such a way that each interval contains a similar number of values, making the data easier to analyze.
For example, if the range of the data (the difference between the largest and smallest values) is 100 and you want to divide the data into 10 classes, the class width would be: Class Width=10010=10\text{Class Width} = \frac{100}{10} = 10
This means each class will cover a range of 10 units. The first class could be 0-10, the second 10-20, and so on.
If the data has already been divided into classes, then you can find the class width by subtracting the lower limit of a class from its upper limit. For instance, if the first class is 10-20, the class width is: Class Width=20−10=10\text{Class Width} = 20 – 10 = 10
Importance of Class Width:
- It ensures the proper grouping of data, making the analysis easier and more understandable.
- A consistent class width allows for accurate graphical representations, such as histograms, where each bar represents a class interval.
- It helps in determining the appropriate number of classes to use, ensuring that the data is not too clustered or too spread out.