Data on the gasoline tax per gallon (in cents) as of a certain date for the 50 U.S. states and the District of Columbia are shown below.
State
Gasoline Tax
per Gallon
State
Gasoline Tax
per Gallon
Alabama
19.1
Missouri
17.4
Alaska
8.9
Montana
27.9
Arizona
19.1
Nebraska
27.8
Arkansas
21.7
Nevada
23.9
California
37.3
New Hampshire
23.9
Colorado
23.2
New Jersey
14.5
Connecticut
24.9
New Mexico
19.0
Delaware
22.9
New York
33.9
District of
Columbia
23.4
North Carolina
35.2
North Dakota
22.9
Florida
30.7
Ohio
27.9
Georgia
26.6
Oklahoma
17.1
Hawaii
18.4
Oregon
30.1
Idaho
33.1
Pennsylvania
51.5
Illinois
33.0
Rhode Island
34.0
Indiana
28.9
South Carolina
16.9
Iowa
31.7
South Dakota
30.1
Kansas
24.9
Tennessee
21.3
Kentucky
25.9
Texas
20.1
Louisiana
20.8
Utah
30.2
Maine
31.5
Vermont
30.6
Maryland
32.9
Virginia
16.9
Massachusetts
26.6
Washington
44.7
Michigan
31.0
West Virginia
33.1
Minnesota
30.7
Wisconsin
32.8
Mississippi
18.3
Wyoming
24.1
(a)
The smallest value in the data set is 8.9 (Alaska) and the largest value is 51.5 (Pennsylvania). Are these values outliers?
Neither Alaska nor Pennsylvania are outliers.
Pennsylvania is an outlier, but Alaska is not.
Alaska and Pennsylvania are both outliers.
Alaska is an outlier, but Pennsylvania is not.
How do you know if they are outliers?
To be an outlier, an observation has to be greater than or less than .
(b)
Construct a boxplot of the data set.
The box-and-whisker plot has a horizontal axis numbered from 0 to 60. The box-and-whisker is also horizontal. The left whisker is approximately 14.5, the left edge of the box is approximately 23.8, the line inside the box is approximately 27.9, the right edge of the box is approximately 33.5, and the right whisker is approximately 44.7. There are 2 outliers located at 8.9 and 51.5.
The box-and-whisker plot has a horizontal axis numbered from 0 to 60. The box-and-whisker is also horizontal. The left whisker is approximately 14.5, the left edge of the box is approximately 25.8, the line inside the box is approximately 31.6, the right edge of the box is approximately 36.5, and the right whisker is approximately 51.5. There is one outlier located at 8.9.
The box-and-whisker plot has a horizontal axis numbered from 0 to 60. The box-and-whisker is also horizontal. The left whisker is approximately 8.9, the left edge of the box is approximately 20.8, the line inside the box is approximately 26.6, the right edge of the box is approximately 31.5, and the right whisker is approximately 44.7. There is one outlier located at 51.5.
The box-and-whisker plot has a horizontal axis numbered from 0 to 60. The box-and-whisker is also horizontal. The left whisker is approximately 8.9, the left edge of the box is approximately 15.8, the line inside the box is approximately 26.6, the right edge of the box is approximately 36.5, and the right whisker is approximately 51.5.
Comment on the interesting features of the plot. (Round numerical answers to the nearest cent.)
The boxplot shows that a typical gasoline tax is around cents per gallon, that the middle 50% of gasoline taxes lie between 21 and cents per gallon, and that the distribution is . There outlier(s) in the distribution.