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

Larson 8th Edition

Ch. 2 - Descriptive Statistics

Problem 2.RE.5

Chapter 2, Problem 2.RE.5

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.

Verified step by step guidance

Step 1: Determine the range of the data set. To do this, subtract the smallest value from the largest value in the data set. The smallest value is 79, and the largest value is 166. Compute the range as: Range = 166 - 79.

Step 2: Calculate the class width. Divide the range by the number of classes (6 in this case) and round up to the nearest whole number. Use the formula: Class Width = ⌈Range / Number of Classes⌉.

Step 3: Create the class intervals. Start with the smallest value (79) as the lower limit of the first class. Add the class width to determine the upper limit of the first class. Repeat this process to create six consecutive, non-overlapping classes.

Step 4: Tally the data into the classes to construct the frequency distribution. Count how many data points fall into each class interval and record the frequencies.

Step 5: Draw a frequency polygon. Plot the midpoints of each class interval on the x-axis and the corresponding frequencies on the y-axis. Connect the points with straight lines to form the polygon. Ensure to include points at the beginning and end of the graph to close the polygon.

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Key Concepts

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

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into classes or intervals, showing the number of observations (frequency) that fall within each class. This helps in understanding the distribution of data points and identifying patterns or trends.

Classes and Class Width

Classes are the intervals into which data is grouped in a frequency distribution. The class width is the range of values that each class covers, calculated by subtracting the lower limit of a class from its upper limit. Choosing an appropriate number of classes and class width is crucial for accurately representing the data.

Frequency Polygon

A frequency polygon is a graphical representation of a frequency distribution. It is created by plotting the midpoints of each class against their corresponding frequencies and connecting these points with straight lines. This visual tool helps to easily identify trends and the overall shape of the data distribution.

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Creating Frequency Polygons

Related Practice

Textbook Question

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.

67 72 88 73 99 85 81 87 63 94 68 87

d. Display the data in a stem-and-leaf plot. Use one line per stem.

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.

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.

Textbook Question

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 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 1 and 2, use the data set, which represents the overall average class sizes for 20 national universities. (Adapted from Public University Honors)

37 34 42 44 39 40 41 51 49 31

52 26 31 40 30 27 36 43 48 35

Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency.

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