Exam 2: Graphical Methods for

As part of the United States Census, data is collected on the number of persons in eachhousehold. The census data for four decades are summarized below.(a) In a few sentences describe how theproportion of households with 4people has changed from 1970 to 2000. (b) What size of household appears to have decreased the most from 1970 to 2000?

A study by the National Bureau of group. The three application strategiesidentified are: apply to a range ofcolleges, some selective some not; applyto no selective colleges; or, finally, use amix of other strategies, such asand one non-selective college.The percentages of students usingthese strategies, broken down byincome, is shown in the table andapplying to one selective college the segmented bar chart.In a few sentences describe howthe college application strategiesdiffer for the low, middle, andhigh income groups.

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

It is well known that the order of the questions in a survey can affect the responses.This is thought to occur because issues raised in one question are remembered whenresponding to later questions. In 1948 many people in the United States wereconcerned about the spread of communism as a political and economic philosophy. Asurvey given that year contained both of the following questions:(i) Do you think the United States should let Communist newspaper reportersfrom other countries come in here and send back to their papers the news asthey see it? (ii) Do you think a Communist country like Russia should let Americannewspaper reporters come in and send back to America the news as they seeit? The following table contains the percentages of the Yes/No answers to question (i)given by respondents when asked these questions in different orders.Responses to Communist reporter question in 1948 (a) Construct a comparative bar chart using these response percentages. (b) Do you think the order of the questions made a difference in the responses? Explain why or why not in a few sentences.

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

An outlier is a data value that is unusually far from the rest of the valuesin a data set.

A report in the Des Moines Register presented on the percentages of students whoqualify for Free/Reduced lunch programs in the elementary schools in Des Moines,Iowa. These data appear in the table below. (a) Sketch a histogram for these data, using the following class intervals:0 to < 2020 to < 40, etc.(b) Describe the distribution of Free/Reduced eligibility percents, and note anyunusual features.

Artificial bird nests have been used extensively when studying predator behavior.Biologists have assumed predators will find and respond to artificial and natural nestsin the same way. In a study to test this assumption the predation of 27 AmericanRobin (Turdus migratorius) nests and 27 artificial wicker-basket nests werecompared. Artificial nests were placed 30m from existing robin's nests in a randomlychosen direction. The natural nests and artificial nests were checked at 5-dayintervals, and the number of nests (out of 27) that had been disturbed by predators inthe interval was noted. The results are as follows: (a) Using a single set of axes, construct time series plots for (a) the number of naturalnests disturbed by predators and (b) the number of artificial nests disturbed bypredators.(b) Does it appear that the artificial and natural nests have the same pattern ofpredation through time? Justify your answer by appealing to specific aspects ofyour plot in part (a).

During the first six months of the American Civil War, armies were amassed as neverbefore in history. Large groups of men, transported far from home, lived inconditions that bred sickness. In a recent study involving Confederate muster rolls, aresearcher constructed a cumulative relative frequency distribution of the percentagesof Confederate soldiers reported sick for each company. A "Company" is a unit ofsoldiers, usually between about 70 and 120 in size. The cumulative relativefrequency distribution for October, 1861, is shown below. (a) Approximately what proportion of the Confederate companies had less than 10%sick? (b) Approximately w hat proportion of the Confederate companies had more than 30%sick? (c) Approximately 50% of the companies had less than what percentage of soldierssick?

One of the "media messages" sent by television is that appearance is very important.These messages are thought to spur young women to have unrealistic expectationsabout beauty, thus encouraging women to spend more money on cosmetics andtoiletries. During a recent prime-time television season investigators kept track of"appearance" comments. Data on comments by TV males, classified by gender of thecomment recipient and type of appearance comment, are given in the table below. (a) Graphically present these data by constructing a comparative bar chart that wouldallow you to compare the comments about males and females.(b) Using the information in the table, write a few sentences about how thecomments differ for male recipients and female recipients.

It is well known that the order of the questions in a survey can affect the responses.This is thought to occur because issues raised in one question are remembered whenresponding to later questions. In 1974 a survey asked the following questions aboutdoctors and lawyers: 1. Would you say that most doctors in this country are really interested in thepublic good, or are most doctors just out to make a lot of money?

A univariate data set must contain numerical, not categorical, data.

Information about the Spanish missions displays two time series of the numbersof baptisms at two Central Bajamissions, San Jose de Comondu and SanGertrudis.In a short paragraph describe and compare the trends in the number of baptisms forthe two missions in this time period, noting any interesting features apparent in theplots.

A segmented bar chart uses rectangles rather than circles to displaydifferent categories in a set of data.

The stem-and-leaf plot below displays the weights (in ounces) for a random sample oftomatoes grown on a local farm (a) Briefly describe the distribution of tomato weights.(b) What is the weight of the heaviest tomato in the sample?

During the first six months of the American Civil War, armies were amassed as neverbefore in history. Large groups of men, transported far from home, lived inconditions that bred sickness. In a recent study involving Confederate muster rolls, aresearcher constructed a cumulative relative frequency distribution of the percentagesof Confederate soldiers reported sick for each company. A "Company" is a unit ofsoldiers, usually between about 70 and 120 in size. The cumulative relativefrequency distribution for December, 1861, is shown below. (a) Approximately what proportion of the Confederate companies had less than 10%sick? (b) Approximately wh at proportion of the Confederate companies had more than 30%sick? (c) Approximately 50% of the companies had less than what percentage of soldierssick?

A report in the Des Moines Register presented the average number of years ofteaching experience for the teachers in elementary schools in Des Moines, Iowa.These data appear in the table below. (a) Sketch a histogram for these data, using the following class intervals:0 to < 44 to < 8, etc.(b) Describe the distribution of the average number of years of teaching experience,and note any unusual features.problem #2 also reported thepercent of children eligible forFree and Reduced lunch to teacherexperience. The percent ofchildren eligible for Free/Reducedlunch is an indicator of the socio

Hoofed animals such as cattle and sheep are classified as browsers (leaf eaters) andgrazers (grass eaters). Some biologists believe that the incisor arcade of the teeth,diagrammed below, is shaped differently for browsers and grazers, affecting theirfood selection. The "curvature" of an incisor arcade is a measure of its shape; largevalues indicate a longer, thinner mouth and small values a shorter, wider mouth. Theback-to-back stem-and-leaf plot below compares the curvatures of incisor arcades fordifferent species of browsers and grazers. (b) Some biologists believe browsers have thinner mouths because leafed plantsfrequently have thorns and spines. They think that browsers have evolved thinnermouths to get beyond the thorns and spines to the food part of the plant. Are thedata in the back-to-back stem-and-leaf plot consistent with this theory? Justifyyour answer by appealing to specific aspect(s) of the plot.

The average circumferences (distances around) in mm of the humerus, femur, and tibiaof different species of mammals are displayed below. These long bones primarilysupport the body mass in mammals. Each data value is the mean circumference forthe available measures for a single species.the distributions of these different bones.(a) Describe the differences and similarities in (b) Biologists speculate that greater weights might be supported by larger bones. Based onthe histograms, if the biologists' speculationsare correct, which of these bones (humerus,femur, or tibia) would seem to be the leastable to support a large weight? Explain,referring to specific aspects of the histograms.

A unimodal set of data is one that contains only one variable.