Exam 3: Graphical Methods for Describing Data

In the article, "Scaling of Mammalian Long Bones: Small and Large Mammals Compared," the average circumferences (distances around)in mm of the humerus, femur, and tibia of different species of mammals were reported.These are the long bones that primarily support the body mass in mammals.Each data value is the mean circumference for the available measures for a single species.

The stem plot below displays the weights (in ounces)of a random sample of tomatoes grown on a local farm

The pie chart below summarizes the results of a survey of 300 randomly selected students at a particular high school.The investigators asked about soft drink preferences at a local high school.

Investigators studying the relation between gender and the interests of early adolescents asked boys and girls in grades 5-9 to indicate on a 7-point scale their degree of interest in topics such as Life, Sports, and Cars. The data in the scatter plot represent average levels of interest for boys and girls in grades 5 - 9.Each point represents one topic listed by the investigators.For example, boys average rating for "Opposite sex" as a 6.2, while girls on average rated their interest in this topic as 6.0 on the 7 point interest scale.This is recorded as the point (6.2, 6.0). There are three interesting features of this scatter plot that you are to interpret below. What can you infer from each of these features of the scatterplot?

An experiment was performed to determine which brand of comparably priced light bulbs, A or B, lasts longer on average.Ten bulbs of each brand were tested, and their lifetimes recorded in hours.The data are shown below:

One of the "media messages" sent by television is that appearance is a very important aspect of one's being.These messages are thought to spur young women to have unrealistic expectations about beauty, thus spending billions of dollars on cosmetics and toiletries.Some of these messages were studied during the 1999-2000 prime- time television season, when investigators kept track of the "appearance" comments. Some of their data, comments by males, classified by gender of recipient and type of appearance comment, is reproduced in the table below.

An outlier is an unusually small or large data value.

As part of the United States Census, data is also collected on the number of persons in each household.The census data for four decades is summarized below.

One advantage of histograms is that they may be used for large data sets.

A curve with tails that decline more rapidly than the tails of a normal curve is called a heavy-tailed distribution.

In a scatter plot, both the horizontal and vertical axes must be set at zero.

Iowa is an agricultural state with a large number of rivers.The use of chemical pesticides and increasing size of livestock herds has created a concern for the water quality in the state.A researcher recently surveyed the rivers of Iowa and analyzed the concentrations of certain chemicals at different locations in the watersheds of Iowa.The cumulative relative frequency plot below displays the distribution of Nitrogen concentrations along the Cedar River.

The density of a class can be calculated by multiplying the relative frequency of the class times the class width.

A statewide survey released by the University of Iowa Injury Prevention Research Center was designed to assess compliance with Iowa seatbelt law.The table at right shows the results for 5 Iowa cities. compared for the different cities. observe in your bar chart for part (a).

Ruminants are hoofed animals such as cattle and sheep.Two categories of ruminants are browsers (leaf eaters)and grazers (grass eaters).Some biologists believe that the incisor arcade, that part of the mouth between the incisors, is shaped differently for browsers and grazers, and that might explain their food selection.The "curvature" of an incisor arcade is a measure of its shape, with large values indicating a long, thin mouth, and small values a shorter, wider mouth.The back-to-back stem plot below compares the curvatures of incisor arcades of a sample of species of browsers and grazers in the ruminant family.

If the upper tail of a distribution stretches out farther than the lower tail, the distribution is negatively skewed.

For stem and leaf plots with single-digit leaves, commas must be used to separate the leaves.

A pie chart is most useful for numeric data.