The Partially Filled Contingency Table Gives The Relative Frequencies Of The Data On Age (in Years) And Sex From The Residents Of A Retirement Home.$[ \begin{tabular}{|l|c|c|c|l|} \hline & 60 − 69 60-69 60 − 69 & 70 − 79 70-79 70 − 79 & Over 79 & Total \ \hline Male & 0.19
Introduction
A contingency table is a statistical tool used to display the relationship between two categorical variables. In this case, we have a partially filled contingency table that provides the relative frequencies of the data on age (in years) and sex from the residents of a retirement home. The table is incomplete, but we can still extract valuable information from it. In this article, we will analyze the table, discuss the implications of the data, and provide insights into the distribution of age and sex in the retirement home.
The Contingency Table
| 60-69 | 70-79 | Over 79 | Total | |
|---|---|---|---|---|
| Male | 0.19 | 0.25 | 0.16 | 0.60 |
| Female | 0.21 | 0.30 | 0.10 | 0.61 |
| Total | 0.40 | 0.55 | 0.26 | 1.21 |
Understanding the Data
The contingency table shows the relative frequencies of the data on age and sex from the residents of a retirement home. The table is divided into three age groups: 60-69, 70-79, and over 79. The rows represent the sex of the residents, and the columns represent the age groups. The table also includes a total row and column, which represents the sum of the relative frequencies for each age group and sex.
Analyzing the Data
From the table, we can see that the majority of the residents are female, with a relative frequency of 0.61. The age group with the highest relative frequency is 70-79, with a frequency of 0.55. The age group with the lowest relative frequency is over 79, with a frequency of 0.26.
Calculating the Relative Frequencies
To calculate the relative frequencies, we need to divide the number of residents in each age group and sex by the total number of residents. Let's assume that the total number of residents is 121 (based on the total row and column).
| 60-69 | 70-79 | Over 79 | Total | |
|---|---|---|---|---|
| Male | 0.19/0.60 = 0.317 | 0.25/0.60 = 0.417 | 0.16/0.60 = 0.267 | 0.60 |
| Female | 0.21/0.61 = 0.344 | 0.30/0.61 = 0.492 | 0.10/0.61 = 0.164 | 0.61 |
| Total | 0.40/1.21 = 0.330 | 0.55/1.21 = 0.455 | 0.26/1.21 = 0.215 | 1.21 |
Interpreting the Results
The relative frequencies show that the majority of the residents are female, with a relative frequency of 0.61. The age group with the highest relative frequency is 70-79, with a frequency of 0.55. The age group with the lowest relative frequency is over 79, with a frequency of 0.26.
Conclusion
In conclusion, the partially filled contingency table provides valuable information about the distribution of age and sex in a retirement home. The table shows that the majority of the residents are female, with a relative frequency of 0.61. The age group with the highest relative frequency is 70-79, with a frequency of 0.55. The age group with the lowest relative frequency is over 79, with a frequency of 0.26.
Recommendations
Based on the analysis of the contingency table, we can make the following recommendations:
- The retirement home should consider providing more services and amenities for the residents in the 70-79 age group, as they have the highest relative frequency.
- The retirement home should also consider providing more support and care for the residents in the over 79 age group, as they have the lowest relative frequency.
- The retirement home should consider increasing the number of female staff members, as the majority of the residents are female.
Limitations
The contingency table has some limitations. The table is partially filled, which means that some of the data is missing. Additionally, the table only provides relative frequencies, which may not be sufficient to make conclusions about the distribution of age and sex in the retirement home.
Future Research
Future research could involve collecting more data on the residents of the retirement home, including their age, sex, and other demographic characteristics. This would allow for a more comprehensive analysis of the distribution of age and sex in the retirement home.
Conclusion
Q: What is a contingency table?
A: A contingency table is a statistical tool used to display the relationship between two categorical variables. In this case, we have a partially filled contingency table that provides the relative frequencies of the data on age (in years) and sex from the residents of a retirement home.
Q: What are the limitations of the contingency table?
A: The contingency table has some limitations. The table is partially filled, which means that some of the data is missing. Additionally, the table only provides relative frequencies, which may not be sufficient to make conclusions about the distribution of age and sex in the retirement home.
Q: How can we interpret the results of the contingency table?
A: The relative frequencies show that the majority of the residents are female, with a relative frequency of 0.61. The age group with the highest relative frequency is 70-79, with a frequency of 0.55. The age group with the lowest relative frequency is over 79, with a frequency of 0.26.
Q: What are the implications of the data?
A: The data suggests that the retirement home should consider providing more services and amenities for the residents in the 70-79 age group, as they have the highest relative frequency. The retirement home should also consider providing more support and care for the residents in the over 79 age group, as they have the lowest relative frequency.
Q: How can we use the contingency table to make recommendations?
A: Based on the analysis of the contingency table, we can make the following recommendations:
- The retirement home should consider providing more services and amenities for the residents in the 70-79 age group, as they have the highest relative frequency.
- The retirement home should also consider providing more support and care for the residents in the over 79 age group, as they have the lowest relative frequency.
- The retirement home should consider increasing the number of female staff members, as the majority of the residents are female.
Q: What are the future research directions?
A: Future research could involve collecting more data on the residents of the retirement home, including their age, sex, and other demographic characteristics. This would allow for a more comprehensive analysis of the distribution of age and sex in the retirement home.
Q: How can we use the contingency table to inform policy decisions?
A: The contingency table can be used to inform policy decisions by providing a snapshot of the distribution of age and sex in the retirement home. This information can be used to make informed decisions about the allocation of resources and the provision of services.
Q: What are the benefits of using a contingency table?
A: The benefits of using a contingency table include:
- It provides a clear and concise way to display the relationship between two categorical variables.
- It allows for the identification of patterns and trends in the data.
- It can be used to make informed decisions about the allocation of resources and the provision of services.
Q: What are the challenges of using a contingency table?
A: The challenges of using a contingency table include:
- It can be difficult to interpret the results, especially if the table is large or complex.
- It may not be possible to make conclusions about the distribution of age and sex in the retirement home if the table is partially filled.
- It may not be possible to make recommendations based on the data if the table is incomplete.