4D

a semispherical map of the world A calculator that has a display reading "tax" sitting on top of 100 dollar bills.Two box plots. The horizontal axis is labeled "Household Tax Costs ($ thousands) and is numbered in increments of one. The top is labeled A and has its lowest point at zero and its highest at approximately 2.3. The lower end of the box is at approximately 0.5 while the upper end is at approximately 2. The center line is at approximately 1.4. For plot B, the lowest point is at 0 and the highest point is at approximately 1.25. The low end of the box is at approximately 0.05 while the upper end is at approximately 0.5. The middle line is at approximately 0.1. Above the high point of plot B, there are lots of individual dots very close together all the way up the rest of the box plot. Two side-by side boxplots. The horizontal axis is labeled "Hate crimes per 100,000 population. On the vertical axis, the first boxplot is labeled "Federal Bureau of Investigation (FBI)" and the second is labeled "Southern Poverty Law Center (SPLC)." For the FBI boxplot, the low point is at zero and the high point is at approximately 0.15. The low end of the box is at approximately 0.03, the high end is at approximately 0.1, and the middle line is at approximately 0.05. There is also a point at approximately 0.3. For the SPLC boxplot, the low point is at approximately .15 and the high point is at approximately 0.2. The low end of the box is at approximately 0.15, the high end is at approximately 0.40, and the center line is at approximately 0.25. There are also two points, one at approximately 0.85 and one at approximately 1.55. A vertical boxplot titled "Percentage of drivers involved in fatal collisions who were alcohol-impaired." The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there are points at16, 41, 42, and 44. The point at 44 is labeled "A." The high point of the box plot is at 38 and labeled "B," while the low point is at 23 and labeled "F." The high end of the box is at 33 and labeled "C" while the low end is at 28 and labeled "E." The middle line is at 30 and labeled "D." A vertical boxplot titled "Percentage of drivers involved in fatal collisions who were alcohol-impaired." The vertical axis is numbered by increments of 5 from 15 to 50. On the graph, there is a point at 16 labeled "D." There are also points at 41, 42, and 44 collectively labeled "A." The high point of the box plot is at 38 and labeled "B," while the low point is at 23 and labeled "C." The high end of the box is at 33 while the low end is at 28. The middle line is at 30.

Country Population Rank GDP per Capita
China 1 $9,771
India 2 $2,016
United States 3 $62,641
Indonesia 4 $3,894
Pakistan 5 $1,473
Brazil 6 $8,921
Nigeria 7 $2,028
Bangladesh 8 $1,698
Russia 9 $11,289
Japan 10 $39,287
Income Group Mean Tax Cut
Lowest Quintile $40
Second Quintile $320
Middle Quintile $780
Fourth Quintile $1,480
Top Quintile $5,790
Top 1 Percent $32,650
Top 0.1 Percent $89,060
state_abbrev median_house_inc hate_crimes_per_100k_splc avg_hatecrimes_per_100k_fbi
AL 42278 0.125838926 1.806410489
AK 67629 0.143740118 1.656700109
AZ 49254 0.225319954 3.413927994
AR 44922 0.069060773 0.869208872
CA 60487 0.255805361 2.397985899
CO 60940 0.390523301 2.804688765
CT 70161 0.335392269 3.772701469
DE 57522 0.322754169 1.469979563
DC 68277 1.52230172 10.95347971
Minimum First

Quartile

 Median Third

Quartile

 Maximum
16 28 30 33 44
Term Boxplot Feature
Minimum
First quartile (Q1)
Median
Third quartile (Q3)
Maximum
Term Boxplot Feature
Upper outlier(s)
Lower outlier(s)
Greatest value of an observation that is not an upper outlier
Lowest value of an observation that is not a lower outlier
State Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol State Percentage of Drivers Involved in Fatal Crashes and Impaired by Alcohol
Utah 16 Maine 30
Kentucky 23 New Hampshire 30
Kansas  24 Vermont 30
Alaska 25 Mississippi 31
Georgia 25 North Carolina 31
Iowa 25 Pennsylvania 31
Arkansas 26 Maryland 32
Oregon 26 Nevada 32
District of Columbia 27 Wyoming 32
New Mexico 27 Louisiana 33
Virginia 27 South Dakota 33
Arizona 28 Washington 33
California 28 Wisconsin 33
Colorado 28 Illinois 34
Michigan 28 Missouri 34
New Jersey 28 Ohio 34
West Virginia 28 Massachusetts 35
Florida 29 Nebraska 35
Idaho 29 Connecticut 36
Indiana 29 Rhode Island 38
Minnesota 29 Texas 38
New York 29 Hawaii 41
Oklahoma 29 South Carolina 41
Tennessee 29 North Dakota 42
Alabama 30 Montana 44
Delaware 30
Boxplot Distribution
A boxplot numbered in increments of 50 from 0 to 350. The low point of the plot is at 50 and the high point is at approximately 290. The low end of the box is at approximately 140, the high end is at approximately 210, and the middle line is at approximately 180. There is also a point at 0 and one at approximately 340. a) left skewed

b) symmetric

c) right skewed
A boxplot numbered in increments of 5 from 0 to 25. The low end of the plot is at 0 and the high end is at approximately 8. The low edge of the box is at approximately 1, while the high edge is at approximately 4 and the center line is at approximately 2. There are also points at approximately 9, 10, 12, 13, 14, 15, 16, 18, 20, 22, and 24. a) left skewed

b) symmetric

c) right skewed
A box plot labeled in increments of 5 from 35 to 60. The low point of the box plot is at 55 and the high point is at approximately 61. The low end of the box is at approximately 56, the high end is at approximately 60, and the middle line is at approximately 58. There are also points at approximately 35, 36, 37, and 38. a) left skewed

b) symmetric

c) right skewed
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Identify the features of a boxplot. 1, 4
Interpret the features of a boxplot. 2
Identify outliers in a dataset. 3, 5
Relate a boxplot of a quantitative variable to its distribution. 6–8

Glossary

first quartile
the value below which one quarter of the data lies, also equal to the 25th percentile. Sometimes denoted Q1.
third quartile
the value below which three quarters of the data lay, also equal to the 75th percentile. Sometimes denoted as Q3.
interquartile range
the quantity Q3–Q1. Sometimes denoted IQR.
five-number summary
the collection of the minimum, first quartile, median, third quartile, and maximum of the variable.
upper outlier
an observation that is greater than Q3 + 1.5 × (IQR).
lower outlier
an observation that is less than Q1 – 1.5 × (IQR).