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
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.6d
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
Verified step by step guidance1
Step 1: Recall the concept of unusual values in statistics. A value is considered unusual if it lies more than 2 standard deviations away from the mean. This is based on the empirical rule for normal distributions.
Step 2: Identify the mean (μ) and standard deviation (σ) of the house prices from the sample statistics provided in Exercise 5. These values are necessary to calculate the range of usual values.
Step 3: Calculate the lower and upper bounds for usual values using the formula: Lower Bound = μ - 2σ and Upper Bound = μ + 2σ. This will give the range within which most house prices are expected to fall.
Step 4: Compare the given house price of \$147,000 to the calculated bounds. If \$147,000 falls outside the range, it is considered unusual; otherwise, it is not unusual.
Step 5: Explain the reasoning based on the comparison. If \$147,000 is outside the bounds, discuss how it deviates significantly from the mean, making it unusual. If it is within the bounds, explain that it is consistent with the expected variation in house prices.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unusual Values
In statistics, an unusual value, often referred to as an outlier, is a data point that significantly differs from the other observations in a dataset. Typically, values that lie beyond 1.5 times the interquartile range (IQR) above the third quartile or below the first quartile are considered unusual. Identifying unusual values helps in understanding the distribution and variability of the data.
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Step 3: Get P-Value
Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. Key measures include the mean, median, mode, range, variance, and standard deviation. These statistics provide insights into the central tendency and dispersion of the data, which are essential for determining whether specific values, like house prices, fall within a typical range.
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Normal Distribution
A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In many cases, house prices can be assumed to follow a normal distribution, allowing for the application of statistical tests to identify unusual values based on standard deviations from the mean.
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Related Practice
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
a. Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.
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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.
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.
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?