Deck 2: Graphical Methods for Describing Data Distributions

Question 1

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

Answer 1

Question 2

In a histogram, class intervals are required to be the same length.

Answer 2

False

Question 3

A pie chart is most useful for numeric data.

Answer 3

False

Question 4

A bar chart is a graphical display of categorical data.

Question 5

A report in the Des Moines Register presented the average number of years of
teaching experience for the teachers in elementary schools in Des Moines, Iowa.
These data appear in the table below. (b) Describe the distribution of the average number of years of teaching experience,
and note any unusual features.

Question 6

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

Question 7

Knowledge of where animals forage for food is essential for effective wildlife
management and conservation. The data below are foraging heights (in m) for a
sample of Mountain Chickadees. The data are taken from two different species of fir
trees: the Douglas fir and the White fir. (a) Display these data using a comparative (back-to-back) stem-and-leaf plot. Use
the stems shown below, and be sure to include all information needed to compare
the two distributions. (b) Compare the distributions in part (a). What differences and similarities do you
observe in the two distributions?
(c) When Mountain Chicadees are sampled to assess their health, they are captured in
mist-nets, which are set to capture the birds at different heights. The mist nets are
about 2 meters high, and directions must be given to the persons who set up the
nests so that the mist-nets are positioned to capture the most birds. Based on the
data from part (a) and your display in part (b), write a short paragraph describing
the appropriate mist-net height in a forest region of Douglas firs and for a forest
region of White firs.

Question 8

Hoofed animals such as cattle and sheep are classified as browsers (leaf eaters) and
grazers (grass eaters). Some biologists believe that the incisor arcade of the teeth,
diagrammed below, is shaped differently for browsers and grazers, affecting their
food selection. The "curvature" of an incisor arcade is a measure of its shape; large
values indicate a longer, thinner mouth and small values a shorter, wider mouth. The
back-to-back stem-and-leaf plot below compares the curvatures of incisor arcades for
different species of browsers and grazers. (a) Briefly describe each distribution, noting any unusual features of the data.
(b) Some biologists believe browsers have thinner mouths because leafed plants
frequently have thorns and spines. They think that browsers have evolved thinner
mouths to get beyond the thorns and spines to the food part of the plant. Are the
data in the back-to-back stem-and-leaf plot consistent with this theory? Justify
your answer by appealing to specific aspect(s) of the plot.

Question 9

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

Question 10

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

Question 11

In a short paragraph describe and compare the trends in the number of baptisms for
the two missions in this time period, noting any interesting features apparent in the
plots.

Question 12

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

Question 13

A time series plot is a graph of data that has been gathered at different
points in time.

Question 14

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

Question 15

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

Question 16

(a) If lesser experienced teachers typical ly teach students from low-income families,
what sort of trend or pattern should appear in the scatter plot?
(b) Does this trend or pattern emerge in these data? Explain, referring to specific
aspects of the scatterplot.

Question 17

When using histograms to compare groups of different sizes, one may
use either frequencies or relative frequencies for the vertical axis and still
be effective.

Question 18

The stem-and-leaf plot below displays the weights (in ounces) for a random sample of
tomatoes grown on a local farm
2L|4 2H| 3L|2 4H|5589 5L|11122334 5H|668999 6L|223344 6H|5556
(a) Briefly describe the distribution of tomato weights.
(b) What is the weight of the heaviest tomato in the sample?

Question 19

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 expectations
about beauty, thus encouraging women to spend more money on cosmetics and
toiletries. During a recent prime-time television season investigators kept track of
"appearance" comments. Data on comments by TV males, classified by gender of the
comment recipient and type of appearance comment, are given in the table below. (a) Graphically present these data by constructing a comparative bar chart that would
allow you to compare the comments about males and females.
(b) Using the information in the table, write a few sentences about how the
comments differ for male recipients and female recipients.

Question 20

A numerical variable is continuous if it's possible values correspond to
isolated points on the number line.

Question 21

Marine biologists have reported the discovery of a new species of fish in the Western
North Atlantic. Data on the head length (n=41) and pelvic fin length (n=30) are
shown below. a) Describe the distributions of these two variables using appropriate statistical
terms.
b) The distribution of head lengths appears to be rather strange. What do you think
might account for the shape of this distribution?

Question 22

During the first six months of the American Civil War, armies were amassed as never
before in history. Large groups of men, transported far from home, lived in
conditions that bred sickness. In a recent study involving Confederate muster rolls, a
researcher constructed a cumulative relative frequency distribution of the percentages
of Confederate soldiers reported sick for each company. A "Company" is a unit of
soldiers, usually between about 70 and 120 in size. The cumulative relative
frequency 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 soldiers
sick?

Question 23

D a) Display these data using a comparative (back-to-back) stem-and-leaf plot. Use the
stems shown below, and be sure to include all information needed to compare the
two distributions.
|1|
|2|
|3|
|4|
|0| |5|
|6|
|7|
|8|
|9|
(b) Describe the similarities and differences between the chosen and not chosen
shelter depths.
(c) Are these data consistent with the researchers' expectations? Explain, using
specific aspect(s) of your plot in part (a).

Question 24

During the first six months of the American Civil War, armies were amassed as never
before in history. Large groups of men, transported far from home, lived in
conditions that bred sickness. In a recent study involving Confederate muster rolls, a
researcher constructed a cumulative relative frequency distribution of the percentages
of Confederate soldiers reported sick for each company. A "Company" is a unit of
soldiers, usually between about 70 and 120 in size. The cumulative relative
frequency 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 soldiers
sick?

Question 25

Investigators were interested in communication about sex and related topics between
parents and 12-14 year olds. The investigators asked parents and students whether or
not they had communicated with their child/parent about topics such as pregnancy,
how to say "no," and methods of contraception. A scatter plot of their data is
presented below. Each point represents one topic listed by the investigators. For
example, 72.4% of parents and 57.6% of adolescents said the parents had discussed
childbirth. This would be recorded as the point (57.6, 72.4). (a) On the graph above, sketch the line y x, representing a line of "perfect
agreement" between the parents and adolescents.
(b) What is a possible explanation of the placement of the points in the scatter plot
relative to the line you sketched in part (a)?

Question 26

As part of the United States Census, data is collected on the number of persons in each
household. The census data for four decades are summarized below. (b) What size of household appears to have decreased the most from 1970 to 2000?

Question 27

a) Display these data using a comparative (back-to-back) stem-and-leaf plot. Use the
stems shown below, and be sure to include all information needed to compare the
two distributions.
|1|
|2|
|3|
|4|
|0| |5|
|6|
|7|
|8|
|9|
(b) Describe the similarities and differences between the chosen and not chosen
shelter depths.
(c) Are these data consistent with the researchers' expectations? Explain, using
specific aspect(s) of your plot in part (a).

Question 28

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 when
responding to later questions. In 1974 a survey asked the following questions about
doctors and lawyers:
1. Would you say that most doctors in this country are really interested in the
public good, or are most doctors just out to make a lot of money?
2. Would you say that most lawyers in this country are really interested in the
public good, or are most lawyers just out to make a lot of money?
The following table summarizes the responses to the lawyer question when these
questions were asked in different orders. (a) Construct a comparative bar chart for these response percentages.
(b) Do you think the order of the questions made a difference in the responses?
Explain.

Question 29

(a) If lesser experienced teachers typical ly teach students from low-income families,
what sort of trend or pattern should appear in the scatter plot?
(b) Does this trend or pattern emerge in these data? Explain, referring to specific
aspects of the scatterplot.

Question 30

Question 31

A report in the Des Moines Register presented on the percentages of students who
qualify 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:
20 t
0 t (b) Describe the distribution of Free/Reduced eligibility percents, and note any
unusual features.

Question 32

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 when
responding to later questions. In 1948 many people in the United States were
concerned about the spread of communism as a political and economic philosophy. A
survey given that year contained both of the following questions:
(i) Do you think the United States should let Communist newspaper reporters
from other countries come in here and send back to their papers the news as
they see it?
(ii) Do you think a Communist country like Russia should let American
newspaper reporters come in and send back to America the news as they see
it?
The following table contains the percentages of the Yes/No answers to question (i)
given by respondents when asked these questions in different orders. (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.

Question 33

The average circumferences (distances around) in mm of the humerus, femur, and tibia
of different species of mammals are displayed below. These long bones primarily
support the body mass in mammals. Each data value is the mean circumference for
the available measures for a single species.