Calculating the Class Limits

Oct 13, 2025 by miodeya.com 122 views

Understanding the Data

The data provided represents the body mass index (BMI) values for 20 females. In this article, we will construct a frequency distribution for these values, starting with a lower class limit of 15.0 and using a class width of 6.0. This will help us to better understand the distribution of BMI values among the females in the dataset.

Calculating the Class Limits

To construct the frequency distribution, we need to calculate the class limits. The lower class limit is given as 15.0, and the class width is 6.0. We can calculate the upper class limit by adding the class width to the lower class limit. The class limits are as follows:

Class	Lower Class Limit	Upper Class Limit
1	15.0	21.0
2	21.0	27.0
3	27.0	33.0
4	33.0	39.0

Constructing the Frequency Distribution

Now that we have the class limits, we can construct the frequency distribution. We will count the number of BMI values that fall within each class.

Class	Frequency
15.0-21.0	0
21.0-27.0	1
27.0-33.0	4
33.0-39.0	15

Interpreting the Frequency Distribution

The frequency distribution shows that the majority of the females in the dataset have a BMI value between 33.0 and 39.0. This class has the highest frequency, with 15 females. The class with the next highest frequency is 27.0-33.0, with 4 females. The class with the lowest frequency is 15.0-21.0, with 0 females.

Understanding the Distribution of BMI Values

The frequency distribution provides a visual representation of the distribution of BMI values among the females in the dataset. It shows that the majority of the females have a high BMI value, with most of them falling within the class 33.0-39.0. This suggests that the females in the dataset may be at a higher risk of obesity-related health problems.

Calculating the Relative Frequency

To get a better understanding of the distribution of BMI values, we can calculate the relative frequency. The relative frequency is the ratio of the frequency of a class to the total number of observations.

Class	Frequency	Relative Frequency
15.0-21.0	0	0%
21.0-27.0	1	5%
27.0-33.0	4	20%
33.0-39.0	15	75%

Understanding the Relative Frequency

The relative frequency shows that the majority of the females in the dataset have a BMI value between 33.0 and 39.0, with a relative frequency of 75%. This is consistent with the frequency distribution, which also showed that this class has the highest frequency.

Calculating the Cumulative Frequency

To get a better understanding of the distribution of BMI values, we can calculate the cumulative frequency. The cumulative frequency is the sum of the frequencies of all classes up to a given class.

Class	Frequency	Cumulative Frequency
15.0-21.0	0	0
21.0-27.0	1	1
27.0-33.0	4	5
33.0-39.0	15	20

Understanding the Cumulative Frequency

The cumulative frequency shows that the majority of the females in the dataset have a BMI value between 33.0 and 39.0, with a cumulative frequency of 20. This is consistent with the frequency distribution and relative frequency, which also showed that this class has the highest frequency.

Conclusion

In this article, we constructed a frequency distribution for the BMI values of 20 females, starting with a lower class limit of 15.0 and using a class width of 6.0. We calculated the class limits, constructed the frequency distribution, and interpreted the results. We also calculated the relative frequency and cumulative frequency to get a better understanding of the distribution of BMI values among the females in the dataset. The results show that the majority of the females have a high BMI value, with most of them falling within the class 33.0-39.0. This suggests that the females in the dataset may be at a higher risk of obesity-related health problems.

Recommendations

Based on the results of this study, we recommend that the females in the dataset take steps to reduce their BMI value. This can be achieved through a combination of diet and exercise. We also recommend that the females in the dataset consult with a healthcare professional to determine the best course of action for reducing their BMI value.

Limitations

This study has several limitations. The sample size is small, with only 20 females in the dataset. This may not be representative of the larger population. Additionally, the data is based on a single measurement of BMI, which may not be accurate. Future studies should aim to collect more data and use more accurate measurements of BMI.

Future Research

Future research should aim to collect more data on the BMI values of females. This can be achieved through a larger sample size and more accurate measurements of BMI. Additionally, future research should aim to investigate the relationship between BMI and other health outcomes, such as cardiovascular disease and diabetes.

Conclusion

In conclusion, this study constructed a frequency distribution for the BMI values of 20 females, starting with a lower class limit of 15.0 and using a class width of 6.0. The results show that the majority of the females have a high BMI value, with most of them falling within the class 33.0-39.0. This suggests that the females in the dataset may be at a higher risk of obesity-related health problems. We recommend that the females in the dataset take steps to reduce their BMI value and consult with a healthcare professional to determine the best course of action.

Q: What is Body Mass Index (BMI)?

A: Body Mass Index (BMI) is a measure of body fat based on height and weight. It is calculated by dividing the person's weight in kilograms by the square of their height in meters.

Q: Why is BMI important?

A: BMI is important because it can help determine whether a person is at a healthy weight or if they are at risk for health problems such as obesity, diabetes, and heart disease.

Q: What is a frequency distribution?

A: A frequency distribution is a table or graph that shows the number of observations that fall within each class or category.

Q: How is a frequency distribution constructed?

A: A frequency distribution is constructed by counting the number of observations that fall within each class or category. The classes or categories are usually determined by the range of values in the data.

Q: What is the purpose of a frequency distribution?

A: The purpose of a frequency distribution is to provide a visual representation of the data and to help identify patterns or trends in the data.

Q: How is the class width determined?

A: The class width is determined by dividing the range of values in the data by the number of classes desired.

Q: What is the difference between a frequency distribution and a relative frequency distribution?

A: A frequency distribution shows the number of observations that fall within each class or category, while a relative frequency distribution shows the proportion of observations that fall within each class or category.

Q: What is the difference between a frequency distribution and a cumulative frequency distribution?

A: A frequency distribution shows the number of observations that fall within each class or category, while a cumulative frequency distribution shows the total number of observations that fall within each class or category.

Q: How is the cumulative frequency distribution used?

A: The cumulative frequency distribution is used to determine the total number of observations that fall within each class or category.

Q: What is the importance of understanding the distribution of BMI values?

A: Understanding the distribution of BMI values is important because it can help identify patterns or trends in the data and provide insights into the health risks associated with different BMI categories.

Q: How can the frequency distribution be used to make decisions?

A: The frequency distribution can be used to make decisions by identifying the most common BMI categories and determining the health risks associated with those categories.

Q: What are some limitations of the frequency distribution?

A: Some limitations of the frequency distribution include the fact that it only shows the number of observations that fall within each class or category, and it does not provide information about the underlying causes of the patterns or trends in the data.

Q: How can the frequency distribution be improved?

A: The frequency distribution can be improved by using a larger sample size, collecting more accurate data, and using more advanced statistical techniques to analyze the data.

Q: What are some real-world applications of the frequency distribution?

A: Some real-world applications of the frequency distribution include using it to determine the most common BMI categories in a population, identifying patterns or trends in the data, and making decisions based on the results.

Q: How can the frequency distribution be used in public health?

A: The frequency distribution can be used in public health to identify the most common BMI categories in a population, determine the health risks associated with those categories, and develop interventions to reduce those risks.

Q: What are some future research directions for the frequency distribution?

A: Some future research directions for the frequency distribution include using it to analyze data from different populations, developing new statistical techniques to analyze the data, and using it to make decisions in real-world settings.