Ch. 2 - Exploring Data with Tables and Graphs

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 2 - Exploring Data with Tables and Graphs

Problem 2.1.14

Chapter 2, Problem 2.1.14

Presidents Listed below are the ages (years) of presidents of the United States at the times of their first inaugurations (from Data Set 22 “Presidents” in Appendix B). Presidents who took office as a result of an assassination or resignation are not included. The data are current as of this writing. Use these ages to construct a frequency distribution. Use a class width of 5 years and begin with a lower class limit of 40 years. Do the ages appear to have a normal distribution?

Verified step by step guidance

Step 1: Organize the data by listing the ages of the presidents at their first inauguration. The ages provided are: 57, 61, 57, 57, 61, 64, 48, 49, 64, 52, 46, 49, 47, 55, 42, 51, 56, 51, 54, 60, 62, 43, 55, 56, 52, 69, 46, 54, 47, 70.

Step 2: Determine the range of the data by identifying the minimum and maximum ages. The minimum age is 42 and the maximum age is 70.

Step 3: Create the class intervals for the frequency distribution. Start with a lower class limit of 40 years and use a class width of 5 years. The classes will be: 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, and 70-74.

Step 4: Count the number of ages that fall into each class interval to construct the frequency distribution. For example, count how many ages fall between 40 and 44, then 45 and 49, and so on.

Step 5: Analyze the frequency distribution to determine if the ages appear to have a normal distribution. A normal distribution typically has a bell-shaped curve, so check if the frequencies increase to a peak and then decrease symmetrically.

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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, allowing for easier analysis of patterns and trends. In this case, the ages of U.S. presidents will be grouped into intervals of 5 years, starting from 40, to visualize the distribution of ages at inauguration.

Class Width

Class width refers to the range of values that each class in a frequency distribution covers. It is calculated by subtracting the lower limit of a class from its upper limit. For this question, a class width of 5 years means that each age group will encompass a range of 5 years, such as 40-44, 45-49, and so on, facilitating the organization of the data.

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. To determine if the ages of presidents exhibit a normal distribution, one would analyze the frequency distribution for symmetry and the presence of a bell-shaped curve, indicating that most ages cluster around the average.

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Related Practice

Textbook Question

In Exercises 9–18, construct the histograms and answer the given questions.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

In Exercises 25 and 26, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated.

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