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Chapter 2: Q.2.42 (page 67)
Identify an important reason for grouping data.
In the event of big data sets, data grouping is important.
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Adjusted Gross Incomes. The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in Statistics of Income, and Individual Income Tax Returns. The following relative frequency histogram shows one year's individual income tax returns for adjusted gross incomes of less than .
Use the histogram and the fact that adjusted gross incomes are expressed to the nearest whole dollar to answer each of the following questions.
a. Approximately what percentage of the individual income tax returns had an adjusted gross income betweenand , inclusive?
b. Approximately what percentage had an adjusted gross income of less than ?
c. The IRS reported that individual income tax returns had an adjusted gross income of less than . Approximately how many had an adjusted gross income between and , inclusive?
RBI Kings, As reported on MLB.com, the five players with the highest runs batted in (RBI) during the 2012 Major League Baseball season are listed in the following table. Also included are the teams for which they played, their positions, and their weights. Identify the type of data provided by the information in each column of the table.
Inauguration Ages. From the Information Please Almanac, we obtained the ages at the inauguration of the first 44 presidents of the United States (from George Washington to Barack H. Obama).
a. Identify the classes for grouping these data, using limit grouping with classes of equal width 5 and a first-class of 40-44.
b. Identify the class marks of the classes found in part (a).
c. Construct frequency and relative frequency distributions of the inauguration ages based on your classes obtained in part (a).
d. Draw a frequency histogram for the inauguration ages based on your grouping in part (a).
e. Classify the shape of the distribution of inauguration ages for the first 44 presidents of the United States both generally and specifically.
Explain the meaning of
a) Qualitative Variable
b) Discrete, Quantitative Variable
c) Continuous, Quantitative Variable
America's Melting Pot. The U.S. Census Bureau publishes data on the population of the United States by race and Hispanic origin in American Community Survey. From that document, we constructed the following bar chart. Note that people who are Hispanic may be of any race, and people in each race group may be either Hispanic or not Hispanic.
a. Explain why a break is shown in the first bar.
b. Why was the graph constructed with a broken bar?
c. Is this graph potentially misleading? Explain your answer.
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