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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 2 - Descriptive StatisticsProblem 2.DS.2c
Chapter 2, Problem 2.DS.2c

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.
Table comparing monthly rental fees in Area A and three other areas, highlighting tenant concerns about high rents.
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 guidance
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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: Mean=∑Rentn, 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: Range=Max-Min. 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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Related Practice
Textbook Question

Extending Concepts


Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.

Midquartile = (Q₁ + Q₃) / 2

In Exercises 55 and 56, find the midquartile of the data set.


5 7 1 2 3 10 8 7 5 3

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Textbook Question

The mean annual salary for a sample of electrical engineers is \$86,500, with a standard deviation of \(1500. The data set has a bell-shaped distribution.


b. The salaries of three randomly selected electrical engineers are \)93,500, \$85,600, and \$82,750. Find the z-score that corresponds to each salary. Determine whether any of these salaries are unusual.

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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.

a. What type of graph would you choose to display the data? Explain your reasoning.

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Textbook Question

Tail lengths (in feet) for a sample of American alligators are listed.

6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6


a. Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning.

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Textbook Question

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130


d. Describe the shape of the distribution as symmetric, uniform, skewed left, skewed right, or none of these.

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Textbook Question

Weekly salaries (in dollars) for a sample of construction workers are listed.

1100 720 1384 1124 1255 976 718 1316

749 1062 1248 891 969 790 860 1100


a. Find the mean, median, and mode of the salaries. Which best describes a typical salary?

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