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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
Chapter 2, Problem 2.R.40

In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency)
36 30 30 45 31 113 113 33 33 33 52 141 56 117 58
118 50 26 23 23 27 48 22 22 22 121 41 105 35 35


About how many vehicles fall on or below the third quartile?

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1
Step 1: Organize the data set in ascending order. This will help in identifying the quartiles accurately. Arrange the given values from smallest to largest.
Step 2: Determine the total number of data points in the set. Count the number of values provided in the data set.
Step 3: Calculate the position of the third quartile (Q3). Use the formula for the position of a quartile: Q3 = (3/4) * (n + 1), where 'n' is the total number of data points.
Step 4: Identify the value corresponding to the third quartile position. If the position is not an integer, interpolate between the two closest values in the ordered data set.
Step 5: Count the number of vehicles with fuel economy values less than or equal to the third quartile value. These are the vehicles that fall on or below the third quartile.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quartiles

Quartiles are values that divide a data set into four equal parts, each containing 25% of the data. The third quartile (Q3) specifically represents the value below which 75% of the data points fall. Understanding quartiles is essential for analyzing the distribution of data, particularly in identifying outliers and understanding the spread of values.
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Data Set

A data set is a collection of related values or observations, often organized in a structured format. In this context, the data set consists of fuel economy values for various vehicles. Analyzing a data set involves calculating measures such as quartiles, means, and medians to summarize and interpret the information it contains.
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Descriptive Statistics

Descriptive statistics are statistical methods that summarize and describe the main features of a data set. This includes measures of central tendency (like mean and median) and measures of variability (like range and quartiles). These statistics provide a quick overview of the data, making it easier to understand trends and patterns, such as how many vehicles fall below a certain quartile.
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Related Practice
Textbook Question

In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League)

8 8 8 6 0 73 26 1

0 5 58 1 7 5 10 63

0 5 10 0 31 5 15 45

16 29 10 73 5 3 0 65


Construct a frequency distribution for the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

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Textbook Question

In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency)

36 30 30 45 31 113 113 33 33 33 52 141 56 117 58

118 50 26 23 23 27 48 22 22 22 121 41 105 35 35


Find the five-number summary of the data set.

89
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Textbook Question

In Exercises 5 and 6, use the data set, which represents the number of rooms reserved during one night’s business at a sample of hotels.


153 104 118 166 89 104 100 79 93 96 116

94 140 84 81 96 108 111 87 126 101 111

122 108 126 93 108 87 103 95 129 93 124


Construct a frequency distribution for the data set with six classes and draw a frequency polygon.

138
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Textbook Question

For the four test scores 96, 85, 91, and 86, the first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores.

124
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Textbook Question

In Exercises 13 and 14, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.


The responses of 1019 adults who were asked how much money they think they will spend on Christmas gifts in a recent year (Adapted from Gallup)


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Textbook Question

In Exercises 25 and 26, find the range, mean, variance, and standard deviation of the population data set.


The mileages (in thousands of miles) for a rental car company’s fleet.

4 2 9 12 15 3 6 8 1 4 14 12 3 3

96
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