How to Find the Class Mark of a Class Interval

Oct 13, 2025 by recoveryshake.com 149 views

Introduction

In statistics, a class interval or class is a range of values that a variable can take. The class mark, also known as the class midpoint, is the value that lies at the center of a class interval. It is an important concept in statistics, as it helps to understand the distribution of data and make informed decisions. In this article, we will learn how to find the class mark of a class interval.

What is a Class Interval?

A class interval is a range of values that a variable can take. It is usually denoted by a lower limit and an upper limit. For example, the class interval $$35.5-45.5$$ means that the variable can take any value between 35.5 and 45.5, inclusive.

Why is the Class Mark Important?

The class mark is an important concept in statistics because it helps to understand the distribution of data. It is used to calculate the mean, median, and mode of a dataset. The class mark is also used in data analysis to identify patterns and trends in the data.

How to Find the Class Mark of a Class Interval

To find the class mark of a class interval, we need to find the midpoint of the interval. The midpoint is the value that lies at the center of the interval. It can be calculated using the following formula:

Class Mark = (Lower Limit + Upper Limit) / 2

Example

Let's find the class mark of the class interval $$35.5-45.5$$. Using the formula above, we get:

Class Mark = (35.5 + 45.5) / 2 = 40.5 / 2 = 20.25

However, the options given in the question are 37.5, 38.5, 39.5, and 40.5. We need to find the correct option.

Step-by-Step Solution

To find the correct option, let's break down the problem step by step.

Find the midpoint of the interval: The midpoint of the interval $$35.5-45.5$$ is the value that lies at the center of the interval. It can be calculated using the formula:

Class Mark = (Lower Limit + Upper Limit) / 2 = (35.5 + 45.5) / 2 = 40.5 / 2 = 20.25
Round the midpoint to the nearest whole number: The options given in the question are 37.5, 38.5, 39.5, and 40.5. We need to round the midpoint to the nearest whole number. Since the midpoint is 20.25, we can round it to 20. However, the options given in the question are not 20, but 37.5, 38.5, 39.5, and 40.5. We need to find the correct option.
Find the correct option: Since the midpoint is 20.25, we can round it to 20. However, the options given in the question are not 20, but 37.5, 38.5, 39.5, and 40.5. We need to find the correct option. Let's try to find the correct option by finding the midpoint of the interval $$35.5-45.5$$.

Class Mark = (Lower Limit + Upper Limit) / 2 = (35.5 + 45.5) / 2 = 81 / 2 = 40.5

The correct option is 40.5.

Conclusion

In this article, we learned how to find the class mark of a class interval. We used the formula Class Mark = (Lower Limit + Upper Limit) / 2 to find the class mark of the class interval $$35.5-45.5$$. We also learned how to round the midpoint to the nearest whole number and find the correct option. The correct option is 40.5.

Frequently Asked Questions

Q: What is a class interval?

A: A class interval is a range of values that a variable can take.

Q: Why is the class mark important?

A: The class mark is an important concept in statistics because it helps to understand the distribution of data. It is used to calculate the mean, median, and mode of a dataset.

Q: How to find the class mark of a class interval?

A: To find the class mark of a class interval, we need to find the midpoint of the interval. The midpoint is the value that lies at the center of the interval. It can be calculated using the formula Class Mark = (Lower Limit + Upper Limit) / 2.

Q: What is the correct option for the class interval $$35.5-45.5$$?

A: The correct option is 40.5.

References

"Statistics for Dummies" by Deborah J. Rumsey
"Mathematics for Dummies" by Mary Jane Sterling
"Statistics: A First Course" by Ronald E. Walpole

About the Author

Frequently Asked Questions

Q: What is a class interval?

A: A class interval is a range of values that a variable can take. It is usually denoted by a lower limit and an upper limit. For example, the class interval $$35.5-45.5$$ means that the variable can take any value between 35.5 and 45.5, inclusive.

Q: Why is the class mark important?

A: The class mark is an important concept in statistics because it helps to understand the distribution of data. It is used to calculate the mean, median, and mode of a dataset. The class mark is also used in data analysis to identify patterns and trends in the data.

Q: How to find the class mark of a class interval?

Q: What is the correct option for the class interval $$35.5-45.5$$?

A: The correct option is 40.5.

Q: Can I use the class mark to calculate the mean of a dataset?

A: Yes, you can use the class mark to calculate the mean of a dataset. The class mark is used to estimate the mean of a dataset when the data is grouped into classes.

Q: How to round the class mark to the nearest whole number?

A: To round the class mark to the nearest whole number, you can use the following rules:

If the decimal part of the class mark is less than 0.5, round down to the nearest whole number.
If the decimal part of the class mark is 0.5 or greater, round up to the nearest whole number.

Q: Can I use the class mark to calculate the median of a dataset?

A: Yes, you can use the class mark to calculate the median of a dataset. The class mark is used to estimate the median of a dataset when the data is grouped into classes.

Q: How to find the class mark of a class interval with a negative lower limit?

A: To find the class mark of a class interval with a negative lower limit, you can use the following formula:

Class Mark = (Lower Limit + Upper Limit) / 2

For example, if the class interval is $$-5.5-0.5$$, the class mark would be:

Class Mark = (-5.5 + 0.5) / 2 = -5 / 2 = -2.5

Q: Can I use the class mark to calculate the mode of a dataset?

A: Yes, you can use the class mark to calculate the mode of a dataset. The class mark is used to estimate the mode of a dataset when the data is grouped into classes.

Q: How to find the class mark of a class interval with a decimal upper limit?

A: To find the class mark of a class interval with a decimal upper limit, you can use the following formula:

Class Mark = (Lower Limit + Upper Limit) / 2

For example, if the class interval is $$35.5-45.5$$, the class mark would be:

Class Mark = (35.5 + 45.5) / 2 = 81 / 2 = 40.5

Q: Can I use the class mark to calculate the standard deviation of a dataset?

A: Yes, you can use the class mark to calculate the standard deviation of a dataset. The class mark is used to estimate the standard deviation of a dataset when the data is grouped into classes.

Conclusion

In this article, we answered some frequently asked questions about the class mark. We covered topics such as what is a class interval, why is the class mark important, how to find the class mark of a class interval, and how to round the class mark to the nearest whole number. We also covered some advanced topics such as how to find the class mark of a class interval with a negative lower limit and how to find the class mark of a class interval with a decimal upper limit.

References

"Statistics for Dummies" by Deborah J. Rumsey
"Mathematics for Dummies" by Mary Jane Sterling
"Statistics: A First Course" by Ronald E. Walpole

About the Author

The author is a mathematics teacher with over 10 years of experience. He has a degree in mathematics and has taught various mathematics courses, including statistics and data analysis. He is passionate about teaching and has written several articles on mathematics and statistics.