2. Describing Data with Tables and Graphs
Visualizing Qualitative vs. Quantitative Data
2:08 minutesProblem 2.DS.2c
Textbook Question
You are a member of your local apartment association. The association represents rental housing owners and managers who operate residential rental property throughout the greater metropolitan area. Recently, the association has received several complaints from tenants in a particular area of the city who feel that their monthly rental fees are much higher compared to other parts of the city.
You want to investigate the rental fees. You gather the data shown in the table at the right. Area A represents the area of the city where tenants are unhappy about their monthly rents. The data represent the monthly rents paid by a random sample of tenants in Area A and three other areas of similar size. Assume all the apartments represented are approximately the same size with the same amenities.
c. Based on your data displays, does it appear that the monthly rents in Area A are higher than the rents in the other areas of the city? Explain.
Verified step by step guidance1
Step 1: Organize the data into a format that allows for comparison. The table already provides monthly rents for Areas A, B, C, and D. Begin by calculating summary statistics for each area, such as the mean, median, and range of rents. These measures will help identify differences in rent levels across the areas.
Step 2: Compute the mean for each area. The mean is calculated by summing all the rent values for a given area and dividing by the number of data points. Use the formula: , where n is the number of apartments sampled.
Step 3: Compute the median for each area. The median is the middle value when the rents are arranged in ascending order. If there is an even number of data points, the median is the average of the two middle values. This measure is less sensitive to extreme values compared to the mean.
Step 4: Calculate the range for each area. The range is the difference between the highest and lowest rent values in each area. Use the formula: . This will provide insight into the variability of rents within each area.
Step 5: Compare the summary statistics (mean, median, and range) across the four areas. If Area A consistently has higher values for these measures compared to Areas B, C, and D, it would suggest that rents in Area A are indeed higher. Additionally, consider creating visualizations such as box plots or histograms to further illustrate the differences in rent distributions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. This includes measures such as mean, median, mode, and standard deviation, which provide insights into the central tendency and variability of the data. In this context, calculating the average rental fees for each area will help determine if Area A's rents are indeed higher than those in Areas B, C, and D.
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Comparative Analysis
Comparative analysis involves evaluating two or more datasets to identify differences and similarities. In this case, comparing the monthly rents across the four areas will help assess whether tenants in Area A are paying significantly more than those in the other areas. This analysis can be visualized through graphs or tables to facilitate understanding of the differences.
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Statistical Significance
Statistical significance determines whether the observed differences in data are likely due to chance or represent a true effect. In this scenario, conducting hypothesis testing (e.g., t-tests) can help ascertain if the higher rents in Area A are statistically significant compared to the other areas, providing a more robust conclusion regarding tenant complaints.
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