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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.37

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.

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Step 1: Organize the data set in ascending order. This is essential for calculating the five-number summary, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
Step 2: Identify the minimum and maximum values in the ordered data set. These are the smallest and largest values, respectively.
Step 3: Calculate the median, which is the middle value of the data set. If the data set has an odd number of values, the median is the middle value. If it has an even number of values, the median is the average of the two middle values.
Step 4: Determine the first quartile (Q1), which is the median of the lower half of the data set (excluding the overall median if the data set has an odd number of values).
Step 5: Determine the third quartile (Q3), which is the median of the upper half of the data set (excluding the overall median if the data set has an odd number of values).

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Key Concepts

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

Five-Number Summary

The five-number summary is a descriptive statistic that provides a quick overview of a data set. It consists of the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. This summary helps to understand the distribution and spread of the data, highlighting its central tendency and variability.
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Quartiles

Quartiles are values that divide a data set into four equal parts, each containing 25% of the data. The first quartile (Q1) is the median of the lower half of the data, while the third quartile (Q3) is the median of the upper half. These measures are essential for understanding the spread and skewness of the data, as they indicate where the bulk of the values lie.
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Median

The median is the middle value of a data set when it is ordered from least to greatest. If the number of observations is odd, the median is the middle number; if even, it is the average of the two middle numbers. The median is a robust measure of central tendency, as it is less affected by outliers compared to the mean.
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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 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.

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


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

Textbook Question

In Exercises 7 and 8, use the data set shown in the table at the left, which represents the pollution indices (a unitless measure of pollution ranging from 0 to 100) for 24 U.S. cities. (Adapted from Numbeo)

Use a dot plot to display the data set. Describe any patterns.

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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