Textbook Question
Refer to the sample statistics from Exercise 5 and determine whether any of the house prices below are unusual. Explain your reasoning.
d. \$147,000
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.Q.1d
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.
Verified step by step guidance1
Step 1: Organize the data set in ascending order to make it easier to analyze the distribution. This helps in identifying patterns or trends in the data.
Step 2: Create a frequency distribution or histogram by grouping the data into intervals (bins). This visual representation will help you observe the shape of the distribution.
Step 3: Analyze the histogram or frequency distribution. Look for symmetry, peaks, and tails. A symmetric distribution will have a bell-shaped curve, while skewed distributions will have longer tails on one side.
Step 4: Calculate measures of central tendency (mean, median, mode) and compare them. If the mean is greater than the median, the distribution is likely skewed right. If the mean is less than the median, the distribution is likely skewed left.
Step 5: Based on the visual representation and the comparison of central tendency measures, describe the shape of the distribution as symmetric, uniform, skewed left, skewed right, or none of these.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distribution Shape
The shape of a distribution refers to the visual representation of data points across a range of values. Common shapes include symmetric, where data is evenly distributed around a central point; skewed left, where more data points fall on the right; and skewed right, where more data points fall on the left. Understanding the shape helps in identifying patterns and making inferences about the data.
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Sampling Distribution of Sample Proportion
Skewness
Skewness measures the asymmetry of a distribution. A distribution is skewed left (negatively skewed) if it has a longer tail on the left side, indicating that most data points are concentrated on the right. Conversely, a right skew (positively skewed) has a longer tail on the right, suggesting that most values are on the left. Identifying skewness is crucial for understanding the data's behavior and potential outliers.
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04:41Creating Frequency Polygons
Descriptive Statistics
Descriptive statistics summarize and describe the main features of a data set. Key measures include the mean, median, mode, and range, which provide insights into the central tendency and variability of the data. These statistics are essential for interpreting the distribution's shape and understanding the overall characteristics of the exercise minutes recorded in the sample.
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05:53Parameters vs. Statistics
Related Practice
Textbook Question
Refer to the sample statistics from Exercise 5 and determine whether any of the house prices below are unusual. Explain your reasoning.
a. \$225,000
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.
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.
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
b. Display the data using a frequency histogram and a frequency polygon on the same axes.
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?