Grouped Frequency Distribution

Oct 13, 2025 by miodeya.com 136 views

Introduction

In a fascinating experiment, a professor asked students to keep track of their social interactions for a week. The data collected from this experiment is presented in the form of a grouped frequency distribution, which provides valuable insights into the number of social interactions that occurred over the week. One of the key aspects of this distribution is the class width, which is a crucial parameter in understanding the data. In this article, we will delve into the concept of class width and determine its value based on the given grouped frequency distribution.

Understanding Class Width

The class width, also known as the class interval or class size, is the difference between the upper and lower limits of a class in a grouped frequency distribution. It represents the range of values that fall within a particular class. In other words, it is the width of each class or interval in the distribution. The class width is an essential component of a grouped frequency distribution, as it helps to identify the range of values that are being represented.

Grouped Frequency Distribution

The grouped frequency distribution of social interactions over the week is presented in the following table:

Class	Frequency
0-5	10
6-10	20
11-15	30
16-20	25
21-25	15
26-30	10
31-35	5
36-40	2
41-45	1

Determining the Class Width

To determine the class width, we need to examine the classes in the distribution and identify the range of values that each class represents. Looking at the table, we can see that the classes are defined as follows:

Class 0-5: 0 to 5
Class 6-10: 6 to 10
Class 11-15: 11 to 15
Class 16-20: 16 to 20
Class 21-25: 21 to 25
Class 26-30: 26 to 30
Class 31-35: 31 to 35
Class 36-40: 36 to 40
Class 41-45: 41 to 45

Calculating the Class Width

Now that we have identified the classes, we can calculate the class width by finding the difference between the upper and lower limits of each class. For example, the class width for the first class (0-5) is 5 - 0 = 5. Similarly, the class width for the second class (6-10) is 10 - 6 = 4, and so on.

Analyzing the Class Widths

Upon analyzing the class widths, we can see that they are not all equal. The class widths vary from 4 to 5, indicating that the classes are not uniform. This is because the data is grouped into classes of varying widths, which can make it difficult to interpret the distribution.

Determining the Class Width

To determine the class width, we need to find the common difference between the class widths. Looking at the table, we can see that the class widths are 5, 4, 4, 4, 4, 4, 4, 4, and 4. The common difference is 4, which means that the class width is 4.

Conclusion

In conclusion, the class width of the social interactions over the week is 4. This value represents the range of values that fall within each class in the grouped frequency distribution. Understanding the class width is essential in interpreting the distribution and gaining insights into the number of social interactions that occurred over the week.

Final Thoughts

The class width is a crucial parameter in understanding the grouped frequency distribution of social interactions over the week. By determining the class width, we can gain valuable insights into the data and make informed decisions. In this article, we have demonstrated how to determine the class width using the given grouped frequency distribution. We hope that this article has provided a clear understanding of the concept of class width and its importance in data analysis.

Introduction

In our previous article, we explored the concept of class width and determined its value based on the grouped frequency distribution of social interactions over the week. In this article, we will address some of the frequently asked questions related to the class width and provide additional insights into the data.

Q&A

Q: What is the purpose of determining the class width?

A: The class width is a crucial parameter in understanding the grouped frequency distribution. It helps to identify the range of values that fall within each class, making it easier to interpret the distribution and gain insights into the data.

Q: How do I determine the class width if the classes are not uniform?

A: If the classes are not uniform, you can calculate the class width by finding the difference between the upper and lower limits of each class. Alternatively, you can find the common difference between the class widths to determine the class width.

Q: Can the class width be any value?

A: No, the class width cannot be any value. It must be a positive integer that represents the range of values that fall within each class.

Q: How do I choose the class width?

A: The class width is typically chosen based on the data and the purpose of the analysis. A common approach is to use a class width that is a multiple of the range of the data.

Q: Can the class width be changed after the data has been grouped?

A: Yes, the class width can be changed after the data has been grouped. However, this may require re-grouping the data and re-calculating the class widths.

Q: What are the advantages of using a uniform class width?

A: Using a uniform class width has several advantages, including:

Easier interpretation of the distribution
Simplified calculations
Improved accuracy

Q: What are the disadvantages of using a non-uniform class width?

A: Using a non-uniform class width has several disadvantages, including:

Difficulty in interpreting the distribution
Increased complexity in calculations
Reduced accuracy

Q: Can the class width be used to compare different distributions?

A: Yes, the class width can be used to compare different distributions. By comparing the class widths, you can identify similarities and differences between the distributions.

Q: How do I determine the class width for a continuous distribution?

A: For a continuous distribution, the class width is typically chosen based on the range of the data and the purpose of the analysis. A common approach is to use a class width that is a multiple of the range of the data.

Q: Can the class width be used to make predictions about the data?

A: Yes, the class width can be used to make predictions about the data. By analyzing the class widths, you can identify patterns and trends in the data that can be used to make predictions.

Conclusion

In conclusion, the class width is a crucial parameter in understanding the grouped frequency distribution of social interactions over the week. By addressing some of the frequently asked questions related to the class width, we hope to have provided additional insights into the data and made it easier to interpret the distribution.

Final Thoughts

The class width is a powerful tool in data analysis, and understanding its importance is essential in making informed decisions. By using the class width to compare different distributions, make predictions about the data, and identify patterns and trends, you can gain valuable insights into the data and make more accurate predictions.