Determining the Class Width

Oct 13, 2025 by windailys.com 71 views

Introduction

In mathematics, a frequency distribution table is a table that displays the frequency of each value in a dataset. It is a useful tool for understanding the distribution of data and identifying patterns or trends. In this article, we will learn how to construct a frequency distribution table for a given dataset using 8 classes.

Understanding the Data

Before we can construct a frequency distribution table, we need to understand the data. Let's assume we have a dataset of exam scores for a class of students. The dataset consists of the following scores:

Score	Frequency
40	2
45	3
50	4
55	5
60	6
65	7
70	8
75	9
80	10
85	11
90	12
95	13
100	14

Determining the Class Width

To construct a frequency distribution table, we need to determine the class width. The class width is the difference between the upper and lower class limits. In this case, we want to use 8 classes, so we need to determine the class width.

To determine the class width, we can use the following formula:

Class width = (Maximum value - Minimum value) / Number of classes

In this case, the maximum value is 100 and the minimum value is 40. We want to use 8 classes, so we can plug these values into the formula:

Class width = (100 - 40) / 8 Class width = 60 / 8 Class width = 7.5

Since we can't have a fraction of a class width, we need to round up to the next whole number. Therefore, the class width is 8.

Constructing the Frequency Distribution Table

Now that we have determined the class width, we can construct the frequency distribution table. We will use the following format:

Class	Frequency	Relative Frequency
40-47
48-55
56-63
64-71
72-79
80-87
88-95
96-100

We will start by filling in the frequency column. We will count the number of scores that fall within each class.

Score	Frequency
40	2
45	3
50	4
55	5
60	6
65	7
70	8
75	9
80	10
85	11
90	12
95	13
100	14

We can see that the following scores fall within each class:

Class	Frequency
40-47	2
48-55	7
56-63	6
64-71	7
72-79	8
80-87	10
88-95	13
96-100	14

Now that we have filled in the frequency column, we can calculate the relative frequency. The relative frequency is the frequency divided by the total number of scores.

Total number of scores = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 94

We can now calculate the relative frequency for each class:

Class	Frequency	Relative Frequency
40-47	2	0.021
48-55	7	0.074
56-63	6	0.064
64-71	7	0.074
72-79	8	0.085
80-87	10	0.106
88-95	13	0.139
96-100	14	0.149

We can round the relative frequency to three decimal places:

Class	Frequency	Relative Frequency
40-47	2	0.021
48-55	7	0.074
56-63	6	0.064
64-71	7	0.074
72-79	8	0.085
80-87	10	0.106
88-95	13	0.139
96-100	14	0.149

Conclusion

In this article, we learned how to construct a frequency distribution table for a given dataset using 8 classes. We determined the class width by using the formula (Maximum value - Minimum value) / Number of classes. We then filled in the frequency column by counting the number of scores that fall within each class. Finally, we calculated the relative frequency by dividing the frequency by the total number of scores. We rounded the relative frequency to three decimal places.

Frequently Asked Questions

Q: What is a frequency distribution table?

A: A frequency distribution table is a table that displays the frequency of each value in a dataset.

Q: How do I determine the class width?

A: To determine the class width, you can use the formula (Maximum value - Minimum value) / Number of classes.

Q: How do I fill in the frequency column?

A: You can fill in the frequency column by counting the number of scores that fall within each class.

Q: How do I calculate the relative frequency?

A: You can calculate the relative frequency by dividing the frequency by the total number of scores.

Q: Why do I need to round the relative frequency to three decimal places?

A: You need to round the relative frequency to three decimal places to make it easier to read and understand.

References

[1] "Frequency Distribution Table." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Frequency_distribution_table.
[2] "Class Width." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Class_width.
[3] "Relative Frequency." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Relative_frequency.
Frequently Asked Questions About Frequency Distribution Tables ================================================================

Q: What is a frequency distribution table?

A: A frequency distribution table is a table that displays the frequency of each value in a dataset. It is a useful tool for understanding the distribution of data and identifying patterns or trends.

Q: How do I determine the class width?

A: To determine the class width, you can use the formula (Maximum value - Minimum value) / Number of classes. For example, if you have a dataset with a maximum value of 100 and a minimum value of 40, and you want to use 8 classes, the class width would be (100 - 40) / 8 = 7.5. Since you can't have a fraction of a class width, you need to round up to the next whole number, which is 8.

Q: How do I fill in the frequency column?

A: You can fill in the frequency column by counting the number of scores that fall within each class. For example, if you have a dataset with the following scores:

Score	Frequency
40	2
45	3
50	4
55	5
60	6
65	7
70	8
75	9
80	10
85	11
90	12
95	13
100	14

You can count the number of scores that fall within each class:

Class	Frequency
40-47	2
48-55	7
56-63	6
64-71	7
72-79	8
80-87	10
88-95	13
96-100	14

Q: How do I calculate the relative frequency?

A: You can calculate the relative frequency by dividing the frequency by the total number of scores. For example, if you have a dataset with a total of 94 scores, and the frequency for each class is:

Class	Frequency
40-47	2
48-55	7
56-63	6
64-71	7
72-79	8
80-87	10
88-95	13
96-100	14

You can calculate the relative frequency for each class by dividing the frequency by the total number of scores:

Class	Frequency	Relative Frequency
40-47	2	0.021
48-55	7	0.074
56-63	6	0.064
64-71	7	0.074
72-79	8	0.085
80-87	10	0.106
88-95	13	0.139
96-100	14	0.149

Q: Why do I need to round the relative frequency to three decimal places?

A: You need to round the relative frequency to three decimal places to make it easier to read and understand. This is because the relative frequency is a decimal value, and rounding it to three decimal places makes it easier to compare and analyze the data.

Q: What are some common mistakes to avoid when constructing a frequency distribution table?

A: Some common mistakes to avoid when constructing a frequency distribution table include:

Not determining the class width correctly
Not filling in the frequency column correctly
Not calculating the relative frequency correctly
Not rounding the relative frequency to three decimal places
Not using a consistent format for the table

Q: How can I use a frequency distribution table in real-world applications?

A: A frequency distribution table can be used in a variety of real-world applications, including:

Analyzing customer data to understand purchasing habits
Identifying trends in stock prices
Understanding the distribution of exam scores
Analyzing the frequency of certain events, such as natural disasters or accidents

Q: What are some advanced techniques for constructing a frequency distribution table?

A: Some advanced techniques for constructing a frequency distribution table include:

Using a histogram to visualize the data
Using a box plot to visualize the data
Using a kernel density estimate to visualize the data
Using a non-parametric test to compare the data to a known distribution

Conclusion

In this article, we have discussed the basics of frequency distribution tables, including how to determine the class width, fill in the frequency column, and calculate the relative frequency. We have also discussed some common mistakes to avoid and some advanced techniques for constructing a frequency distribution table. By following these guidelines, you can create a frequency distribution table that is accurate and informative.