3.19 The article “Frost Belt Feels Labor Drain” (USA Today, May 1, 2008) points out that even though total population is increasing, the pool of young workers is shrinking in many states. This observation was prompted by the data in the accompanying table. Entries in the table are the percent change in the population of 25- to 44-year-olds over the period from 2000 to 2007. A negative percent change corresponds to a state that had fewer 25- to 44-year-olds in 2007 than in 2000 (a de- crease in the pool of young workers).

State                                        % Change

 

Alabama                                                    -4.1

Alaska                                                          -2.5

Arizona                                                         17.8

Arkansas                                                          0.9

California                                                   -0.4

Colorado                                                       4.1

Connecticut                                                -9.9

Delaware                                                    -2.2

(continued)

 

 

 

State                                        % Change

 

District of Columbia	1.8
Florida	5.8
Georgia	7.2
Hawaii	-1.3
Idaho	11.1
Illinois	-4.6

Indiana                                                       -3.1

Iowa                                                           -6.5

 

Kansas	-5.3
Kentucky	-1.7
Louisiana	-11.9
Maine	-8.7
Maryland	-5.7

Massachusetts                                           -9.6

Michigan                                                    -9.1

Minnesota                                                  -4.5

Mississippi                                                 -5.2

Missouri                                                     -2.9

Montana                                                     -3.7

Nebraska                                                    -5.6

Nevada                                                          22.0

 

New Hampshire	-7.5
New Jersey	-7.8
New Mexico	0.6
New York	-8.0
North Carolina	2.4

North Dakota                                          -10.9

Ohio                                                           -8.2

Oklahoma                                                  -1.6

Oregon                                                           4.4

Pennsylvania                                              -9.1

Rhode Island                                              -8.8

South Carolina                                              0.1

South Dakota                                            -4.1

Tennessee                                                      0.6

Texas                                                             7.3

Utah                                                            19.6

Vermont                                                   -10.4

Virginia                                                      -1.1

Washington                                                   1.6

West Virginia                                             -5.4

Wisconsin                                                   -5.0

Wyoming                                                   -2.3

 

a.      The smallest value in the data set is -11.9 and the largest value is 22.0. One possible choice of stems for a  stem-and-leaf  display  would  be  to  use  the  tens digit,  resulting  in  stems  of  -1,  -0,  0,  1,  and  2. Notice that because there are both negative and posi- tive values in the data set, we would want to use two 0  stems—one  where  we  can  enter  leaves  for  the

 

 

Bold exercises answered in back                      Data set available online                    Video Solution available

 

116             Chapter 3 Graphical Methods for Describing Data

 

 

 

negative percent changes that are between 0 and

-9.9, and one where we could enter leaves for the positive percent changes that are between 0 and 9.9. Construct  a  stem-and-leaf  plot  using  these  five stems. (Hint: Think of each data value as having two digits before the decimal place, so 4.1 would be re- garded as 04.1.)

b.       Using two-digit stems would result in more than 30 stems, which is more than we would usually want for a stem-and-leaf display. Describe a strategy for using repeated stems that would result in a stem- and-leaf display with about 10 stems.

c.       The article described “the frost belt” as the cold part of the country—the Northeast and Midwest— noting that states in the frost belt generally showed a decline in the number of people in the 25- to 44-year-old age group. How would you describe the group of states that saw a marked increase in the number of 25- to 44-year-olds?