Understanding the Problem and Creating a Frequency Table

Oct 13, 2025 by talynt.org 110 views

Understanding the Problem and Creating a Frequency Table

The students in Marly's math class recorded the dimensions of their bedrooms in a frequency table. This table is a great way to visualize the data and understand the distribution of bedroom areas. The frequency table is a table that displays the number of times each value occurs in a dataset. In this case, the dataset is the area of the students' bedrooms.

Frequency Table:

Area (sq. ft)	Number of Bedrooms
100-150	5
150-200	8
200-250	3
250-300	2
300-350	1

Analyzing the Frequency Table

The frequency table shows that the majority of the students have bedrooms with areas between 150-200 sq. ft. This is the most common range, with 8 students having bedrooms in this range. The least common range is 300-350 sq. ft, with only 1 student having a bedroom in this range.

Understanding the Distribution of Bedroom Areas

The frequency table also shows that the distribution of bedroom areas is not uniform. The majority of the students have bedrooms with areas between 150-250 sq. ft. This suggests that the students in Marly's math class tend to have smaller bedrooms.

Calculating the Mean and Median of the Bedroom Areas

To further analyze the data, we can calculate the mean and median of the bedroom areas. The mean is the average of the data, while the median is the middle value of the data when it is arranged in order.

Calculating the Mean:

To calculate the mean, we need to multiply each area by its frequency and add up the results. We then divide the sum by the total number of students.

Mean = (5 x 125) + (8 x 175) + (3 x 225) + (2 x 275) + (1 x 325) / 19 Mean = 625 + 1400 + 675 + 550 + 325 / 19 Mean = 3385 / 19 Mean = 178.15

Calculating the Median:

To calculate the median, we need to arrange the data in order and find the middle value. Since there are 19 students, the middle value is the 10th value.

Area (sq. ft): 100-150, 100-150, 100-150, 100-150, 100-150, 150-200, 150-200, 150-200, 150-200, 150-200, 150-200, 200-250, 200-250, 200-250, 250-300, 250-300, 300-350 Median = 175

Interpreting the Results

The mean and median of the bedroom areas are 178.15 sq. ft and 175 sq. ft, respectively. This suggests that the average bedroom area is around 175-180 sq. ft. The frequency table shows that the majority of the students have bedrooms with areas between 150-200 sq. ft, which is consistent with the mean and median values.

Conclusion

In conclusion, the frequency table shows that the majority of the students in Marly's math class have bedrooms with areas between 150-200 sq. ft. The mean and median of the bedroom areas are 178.15 sq. ft and 175 sq. ft, respectively. This suggests that the average bedroom area is around 175-180 sq. ft. The frequency table and the mean and median values provide a comprehensive understanding of the distribution of bedroom areas in the class.

Future Research Directions

Future research directions could include:

Analyzing the relationship between bedroom area and student performance: This could involve collecting data on student performance and analyzing the relationship between bedroom area and performance.
Comparing the distribution of bedroom areas in different classes: This could involve collecting data from different classes and comparing the distribution of bedroom areas.
Investigating the factors that influence bedroom area: This could involve collecting data on factors such as family income, number of siblings, and parental education level, and analyzing the relationship between these factors and bedroom area.

Limitations of the Study

The study has several limitations, including:

Small sample size: The study only includes data from 19 students, which may not be representative of the entire class.
Limited data collection: The study only collects data on bedroom area, which may not be sufficient to understand the distribution of bedroom areas.
Lack of control variables: The study does not control for variables such as family income, number of siblings, and parental education level, which may influence bedroom area.

Recommendations for Future Research

Based on the limitations of the study, the following recommendations are made for future research:

Increase the sample size: Future studies should aim to collect data from a larger sample size to increase the representativeness of the results.
Collect more data: Future studies should collect more data on factors such as family income, number of siblings, and parental education level to understand the relationship between these factors and bedroom area.
Control for variables: Future studies should control for variables such as family income, number of siblings, and parental education level to ensure that the results are not influenced by these factors.

Q: What is a frequency table?

A: A frequency table is a table that displays the number of times each value occurs in a dataset. In this case, the dataset is the area of the students' bedrooms.

Q: What does the frequency table show about the distribution of bedroom areas?

A: The frequency table shows that the majority of the students have bedrooms with areas between 150-200 sq. ft. This is the most common range, with 8 students having bedrooms in this range.

Q: What is the mean of the bedroom areas?

A: The mean of the bedroom areas is 178.15 sq. ft. This is calculated by multiplying each area by its frequency and adding up the results, then dividing the sum by the total number of students.

Q: What is the median of the bedroom areas?

A: The median of the bedroom areas is 175 sq. ft. This is the middle value of the data when it is arranged in order.

Q: What does the mean and median values suggest about the average bedroom area?

A: The mean and median values suggest that the average bedroom area is around 175-180 sq. ft.

Q: What are some potential limitations of the study?

A: Some potential limitations of the study include a small sample size, limited data collection, and lack of control variables.

Q: What are some recommendations for future research?

A: Some recommendations for future research include increasing the sample size, collecting more data, and controlling for variables such as family income, number of siblings, and parental education level.

Q: What are some potential future research directions?

A: Some potential future research directions include analyzing the relationship between bedroom area and student performance, comparing the distribution of bedroom areas in different classes, and investigating the factors that influence bedroom area.

Q: What are some potential applications of this research?

A: Some potential applications of this research include informing school administrators about the distribution of bedroom areas in the class, helping teachers to understand the needs of their students, and providing insights for parents and policymakers.

Q: What are some potential implications of this research?

A: Some potential implications of this research include the potential for schools to provide more support for students with smaller bedrooms, the potential for teachers to tailor their instruction to the needs of their students, and the potential for policymakers to develop more effective policies to address the needs of students with smaller bedrooms.

Q: What are some potential future studies that could build on this research?

A: Some potential future studies that could build on this research include collecting data on student performance and analyzing the relationship between bedroom area and performance, collecting data from different classes and comparing the distribution of bedroom areas, and collecting data on factors such as family income, number of siblings, and parental education level and analyzing the relationship between these factors and bedroom area.

Q: What are some potential challenges that researchers may face when conducting future studies?

A: Some potential challenges that researchers may face when conducting future studies include collecting data from a larger sample size, collecting more data on factors such as family income, number of siblings, and parental education level, and controlling for variables such as family income, number of siblings, and parental education level.

Q: What are some potential benefits of conducting future studies?

A: Some potential benefits of conducting future studies include gaining a deeper understanding of the distribution of bedroom areas in the class, identifying potential factors that influence bedroom area, and developing more effective policies to address the needs of students with smaller bedrooms.