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Statistics in Context

Barbara Blatchley

Chapter 3

A PICTURE IS WORTH A THOUSAND WORDS: CREATING AND INTERPRETING GRAPHICS - all with Video Answers

Educators


Chapter Questions

02:42

Problem 1

Students in an introductory psychology course were asked to participate in an
experiment examining the relationship between quality of sleep and perceived
stress. Each student in the class kept track of the quality of his or her sleep for seven
consecutive days using a 5-point scale where 1 indicated very poor quality, 3 indicated
average quality, and 5 indicated excellent sleep quality for the previous night. At the
end of the week, each student donated a small hair sample consisting of approximately
20 to 30 strands of hair. The level of cortisol in the hair sample was obtained (in
nanograms per gram of hair). Higher levels of cortisol indicate higher levels of stress.
Table 3.5 shows the raw data from the 50 students in the study.
table cant copy
a. Create frequency distributions of both the sleep quality and cortisol levels.
b. Draw a graph showing the distribution of sleep quality in the sample.
c. Draw a graph showing the distribution of cortisol in the hair samples.

Lucas Finney
Lucas Finney
Numerade Educator
04:08

Problem 2

Table 3.6 shows the sleep data we worked with in Chapter 2. Construct a bar chart and
a stem-and-leaf graph for the data. How will you handle the large gaps in the data in
these two types of graphs?
$$
\begin{array}{c|c|c|c}
\text { Minutes } & f & \text { Minutes } & f \\
\hline 120 & 22 & 430 & 1 \\
\hline 275 & 1 & 440 & 1 \\
\hline 330 & 1 & 445 & 1 \\
\hline 340 & 1 & 450 & 5 \\
\hline 360 & 1 & 455 & 1 \\
\hline 375 & 1 & 470 & 1 \\
\hline 380 & 1 & 480 & 1 \\
\hline 385 & 1 & 495 & 1 \\
\hline 390 & 3 & 520 & 1 \\
\hline 405 & 2 & 525 & 1 \\
\hline 420 & 1 & 620 & 1 \\
\hline
\end{array}
$$

KS
Kathleen Snyder
Numerade Educator
02:45

Problem 3

Graph the data shown in Table 3.7 using an appropriate graph type. Then, answer the
questions about the data that follow.
a. Describe the main point of the graph. Construct a grouped frequency distribution
of the data (use 10 beats per minute as your interval size), and graph the grouped
frequency distribution. Which of these two graphs is clearer?
b. Women typically have a faster heart rate than men do. Does the graph suggest that both
men and women are in this data set? What aspect of the graph supports your conclusion?
c. If you have not yet done so, create a stem-and-leaf graph of the data.
$$
\begin{array}{c|c}
\hline \text { ID } & \text { Heart Rate } \\
\hline 1 & 65 \\
\hline 2 & 67 \\
\hline 3 & 85 \\
\hline 4 & 88 \\
\hline 5 & 85 \\
\hline 6 & 56 \\
\hline
\end{array}
$$
$$
\begin{array}{|r|l}
\hline 7 & 96 \\
\hline 8 & 98 \\
\hline 9 & 57 \\
\hline 10 & 92 \\
\hline 11 & 84 \\
\hline 12 & 73 \\
\hline 13 & 80 \\
\hline 14 & 76 \\
\hline 15 & 70 \\
\hline 16 & 56 \\
\hline 17 & 69 \\
\hline 18 & 51 \\
\hline 19 & 75 \\
\hline 20 & 77 \\
\hline 21 & 65 \\
\hline 22 & 74 \\
\hline 23 & 92 \\
\hline
\end{array}
$$

Charles Carter
Charles Carter
Numerade Educator
01:18

Problem 4

Graph the data shown in Table 3.8 using a frequency polygon. (Note that in order to
do this, you’ll have to create a frequency distribution of the data.)

$$
\begin{array}{c|c|c|c}
\hline \text { ID } & \text { Weight } & \text { ID } & \text { Weight } \\
\hline 1 & 19 & 11 & 21 \\
\hline 2 & 17 & 12 & 21 \\
\hline 3 & 20 & 13 & 20 \\
\hline 4 & 20 & 14 & 22 \\
\hline 5 & 16 & 15 & 21 \\
\hline 6 & 19 & 16 & 17 \\
\hline 7 & 19 & 17 & 18 \\
\hline 8 & 16 & 18 & 17 \\
\hline 9 & 19 & 19 & 19 \\
\hline 10 & 19 & 20 & 18 \\
\hline
\end{array}
$$

Julian Wong
Julian Wong
Numerade Educator
06:59

Problem 5

Tramo et al. (1998) examined the surface area of the corpus callosum, a large bundle
of nerve fibers that connects the left and right hemispheres of the brain, in newborn
twins. The data in Table 3.9 are similar to what they found. Create a graph of the frequency distributions for the males and the females.
$$
\begin{array}{c|c|c}
\hline \text { Pair } & \text { Males } & \text { Females } \\
\hline 1 & 7.01 & 5.88 \\
\hline 2 & 6.61 & 7.34 \\
\hline 3 & 7.84 & 6.85 \\
\hline 4 & 6.64 & 7.10 \\
\hline 5 & 6.68 & 7.66 \\
\hline 6 & 6.59 & 6.30 \\
\hline 7 & 7.52 & 7.39 \\
\hline 8 & 7.67 & 7.08 \\
\hline 9 & 6.22 & 7.16 \\
\hline 10 & 7.95 & 6.55 \\
\hline
\end{array}
$$
The mean surface area of the corpus callosum for males is $7.073 \mathrm{~cm}^2$, and the mean surface area for females is $6.931 \mathrm{~cm}^2$. Create a graph of these two means. Do you think these two groups of measurements are meaningfully different?

Vaidik Stats
Vaidik Stats
Numerade Educator
10:07

Problem 6

. Suppose you participated in a study about the effects of stimulating the olfactory system on your ability to concentrate during a visual search task. Subjects are asked to complete a visual search task while smelling either an unpleasant or a pleasant odor. The time needed to complete the visual search task (in seconds) is recorded. Table 3.10 shows this hypothetical data.
$$
\begin{array}{c|c}
\hline \text { Unpleasant Odor } & \text { Pleasant Odor } \\
\hline 65 & 80 \\
\hline 55 & 70 \\
\hline 82 & 63 \\
\hline 42 & 77 \\
\hline 48 & 75 \\
\hline 55 & 71 \\
\hline 71 & 58 \\
\hline 93 & 80 \\
\hline 83 & 71 \\
\hline
\end{array}
$$
$$
\begin{array}{l|c}
\hline 41 & 72 \\
\hline 88 & 85 \\
\hline 78 & 155 \\
\hline 38 & 75 \\
\hline 48 & 66 \\
\hline 91 & 71 \\
\hline 56 & 122 \\
\hline 43 & 69 \\
\hline 60 & 84 \\
\hline 40 & 95 \\
\hline 84 & 70 \\
\hline 57 & 86 \\
\hline 81 & 120 \\
\hline 50 & 96 \\
\hline 68 & 72 \\
\hline
\end{array}
$$
a. Graph the data using the graph type of your choice.
b. Describe the results of this study. Was there a difference in the time needed to
complete the visual search in the two conditions (unpleasant odor vs. pleasant odor)?

DD
Derek Dean
Numerade Educator
02:11

Problem 7

Create a pie chart for the data shown in Table 3.11. If a convict is going to reoffend,
what type of crime is he most likely to commit?
$$
\begin{array}{c|c|c|c}
\hline \text { Violent Offenses } & \text { Property Offenses } & \text { Drug Offenses } & \text { Public Disorder Offenses } \\
\hline 50 & 100 & 335 & 15 \\
\hline
\end{array}
$$

Brandon Cleary
Brandon Cleary
Numerade Educator
12:33

Problem 8

Do you know what a “lug” is? Nope, it’s not a big guy in a movie from the 1940s. It’s a
way to measure grape harvests in a vineyard. A “lug” is a large basket (1.5 feet by 3 feet
by 6 inches) that is placed at the end of a row of grapevines. Workers move down each
row of grapevines and dump the clumps of grapes they pick into the nearest lug. Lug
counts are then used to measure grapevine production for a given harvest. Table 3.12
shows the lug count from a nine-year span at the Château du Plonk winery. Describe
how the harvest changed over these nine years.
$$
\begin{array}{|l|l|l|l|l|l|l|l|l|}
\hline 1983 & 1984 & 1985 & 1986 & 1987 & 1988 & 1989 & 1990 & 1991 \\
\hline 534 & 552 & 401 & 266 & 514 & 377 & 170 & 502 & 940 \\
\hline
\end{array}
$$

Abhishek Jana
Abhishek Jana
Numerade Educator
02:57

Problem 9

How far can the average golfer on the PGA tour drive a golf ball? Here are the average
driving distances for the top 25 drivers on the tour. If you go looking for this statistic,
you’ll quickly realize that it changes almost weekly as players vie for the top spot on
this list in each tournament.
a. Are there any outliers in this distribution?
b. Create a graph of the data. (To make it easier, round the distances to the nearest
whole number.)
c. What is the length of a “typical” drive for these 25 players?
$$
\begin{array}{l|l|l|l}
\hline \text { Rank) Name } & \text { Distance } & \text { Rank) Name } & \text { Distance } \\
\hline \text { 1) B. Watson } & 315.1 & \text { 14) K. Bradley } & 298.6 \\
\hline \text { 2) J. Lovemark } & 309.9 & \text { 15) A. Cabrera } & 297.7 \\
\hline \text { 3) R. Garrigus } & 306.6 & \text { 16) B. Gates } & 297.6 \\
\hline \text { 4) D. Johnson } & 305.9 & \text { 17) S. Piercy } & 297.3 \\
\hline \text { 5) J. Kokrak } & 304.4 & \text { 18) T. Matteson } & 297.0 \\
\hline \text { 6) C. Beljan } & 303.6 & \text { 19) J. Teater } & 296.6 \\
\hline \text { 7)J. B. Holmes } & 302.8 & \text { 20) S.-Y. Noh } & 296.5 \\
\hline \text { 8) K. Stanley } & 302.6 & \text { 21) C. Hoffman } & 296.3 \\
\hline \text { 9) H. English } & 301.3 & \text { 22) T. Kelly } & 295.9 \\
\hline \text { 10) J. Vegas } & 300.9 & \text { 23) B. Jobe } & 295.4 \\
\hline \text { 11) G. DeLaet } & 300.8 & \text { 24) M. Laird } & 295.2 \\
\hline \text { 12) R. Palmer } & 300.3 & \text { 25) T. Gainey } & \\
\hline \text { 13) G. Woodland } & 300.3 & & \\
\hline
\end{array}
$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:56

Problem 10

Graph the driving distances in Table 3.13 using a stem-and-leaf graph.

Brandon Cleary
Brandon Cleary
Numerade Educator
05:11

Problem 11

Remember the question about smoking and mental health from Chapter 2? Table 3.14
shows the frequency distribution data. Create a pie chart for each group (schizophrenics and nonschizophrenics). Write a short description of the smoking behavior in
these two groups of people.

$$
\begin{array}{c|c|c|c}
\hline \text { Schizophrenics } & f & \text { Nonschizophrenics } & f \\
\hline \text { Yes } & 17 & \text { Yes } & 5 \\
\hline \text { No } & 3 & \text { No } & 15 \\
\hline
\end{array}
$$

Robin Corrigan
Robin Corrigan
Numerade Educator
View

Problem 12

When is your birthday? Are you a midwinter baby, or were you born in the heat of
summer? Several studies have suggested a relationship between the season of birth
and psychiatric or neurological disorders. The relationship might be the result of the
influence of the environment and seasonal characteristics like the amount of light
available, temperature, and prevalence of infectious agents on brain development.
Chotai and Wiseman (2005) surveyed almost 30,000 people from 67 countries (75%
from Britain) and asked what month they were born in and how they would respond
to a simple statement: “I am a lucky person.” Their response options were on a scale
from 1 to 5, where 1 = strong disagreement and 5 = strong agreement with the statement. Higher numbers on this scale indicate a stronger belief in luck. The data shown
in Table 3.15 are similar to what Chotai and Wiseman found. Does belief in being
lucky depend on the month in which a person was born?
table cant copy

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:58

Problem 13

Let’s divide the data in Table 3.15 into two sections: Fall/Winter (September through
February) and Spring/Summer (March through August). We will calculate the average
“Belief in Luck” score for each section. To do this, we need to add up the scores for each
month in a given section and then divide the total by the number of months in that section.
$$
\begin{array}{c|c|c|c}
\hline \text { Birth Month } & \text { Belief in Luck } & \text { Birth Month } & \text { Belief in Luck } \\
\hline \text { Sep. } & 3.19 & \text { Mar. } & 3.28 \\
\hline \text { Oct. } & 3.18 & \text { Apr. } & 3.30 \\
\hline \text { Nov. } & 3.20 & \text { May } & 3.33 \\
\hline \text { Dec. } & 3.20 & \text { Jun. } & 3.20 \\
\hline \text { Jan. } & 3.22 & \text { Jul. } & 3.24 \\
\hline \text { Feb. } & 3.22 & \text { Aug. } & 3.21 \\
\hline \text { Total } & 19.21 & \text { Total } & 19.56 \\
\hline \text { Average } & \mathbf{3 . 2 0} & \text { Average } & \mathbf{3 . 2 6} \\
\hline
\end{array}
$$
Now plot the means using a bar chart. Does this new graph change in your interpretation of the data?

Ashley Volpe
Ashley Volpe
Numerade Educator
01:39

Problem 14

Professor Richard Wiseman has been studying belief in luck for quite a while. In 2003,
Professor Wiseman surveyed residents of Britain about their superstitions. Table 3.16
shows results similar to what Professor Wiseman found.
a. Notice that the total number of responses is more than twice the total number of
people surveyed. Why? What does this tell you about belief in superstition?
b. Describe superstitious behavior in British citizens.
table cant copy

Kevin Morgan
Kevin Morgan
Numerade Educator
02:52

Problem 15

The Hermann Grid is a visual illusion created by Ludimar Hermann in 1870.
Hermann found that when observers looked at a grid made of black squares on a white
background, they saw an “illusory dot”—a fuzzy gray dot that actually was not there—
at the intersection of the white lines. One of my students had a great idea: She wanted
to know if the color of the Hermann grid affected the visual illusion (Blatchley &
Moses, 2012). Does the illusory dot disappear if the grid is something other than black
and white? She presented 50 participants with Hermann grids in six colors—black,
red, yellow, green, blue, and purple, all on white backgrounds—and asked the participants if they saw the dot. The data in Table 3.17 are representative of what we found.
table cant copy

Alexander Burbelo
Alexander Burbelo
Numerade Educator
04:55

Problem 16

. How well do you perceive the passage of time? Students in my senior research seminar wanted to know if the perception of time was affected by experience with all of the
labor-saving devices we’re so accustomed to using. We asked participants ranging in age
from 6 to 71 years to complete a short survey measuring their daily computer use and
then to judge the duration of a series of time intervals (3 to 27 seconds in length) without
using a counting method. “Computer Use” (CU) was measured on a scale from 9 to 74:
The higher the number, the more time the participant spent using the computer on a daily
basis. Accuracy in the ability to estimate time intervals was measured by subtracting the
estimated duration of the time interval from the actual time interval: the smaller this error, the more accurate the time estimation. The data in Table 3.18 are representative of
what we found (Blatchley et al., 2007). What can you say about computer use in these age
groups? What can you say about accuracy in time estimation as a function of age?
table cant copy

Neel Faucher
Neel Faucher
Numerade Educator
01:21

Problem 17

Create a scatterplot for the data shown in Table 3.19. The data come from the timeestimation study referenced in question 16. Each row represents two measurements
(age and time-estimation error) taken from 15 of our participants. What can you say
about the relationship between age and accuracy in time estimation?
$$
\begin{array}{c|c}
\hline \text { Age (in Years) } & \text { Error in Time Estimation } \\
\hline 13 & 4.29 \\
\hline 20 & 2.15 \\
\hline 35 & 1.38 \\
\hline 17 & 6.02 \\
\hline 20 & 2.01 \\
\hline 16 & 4.29 \\
\hline 22 & 1.35 \\
\hline 12 & 7.89 \\
\hline 11 & 2.08 \\
\hline 31 & 1.06 \\
\hline 19 & 1.70 \\
\hline 6 & 8.87 \\
\hline 11 & 3.44 \\
\hline 6 & 9.72 \\
\hline 7 & 5.28 \\
\hline
\end{array}
$$

James York
James York
Numerade Educator

Problem 18

Create stem-and-leaf graphs for the grip strength data shown in Table 2.22 (in question 15 of the Chapter 2 practice problems). We want to compare grip strength in "neutral" light and in blue light, so you will need a way to distinguish between the two conditions in your graph (or graphs).

Check back soon!
06:00

Problem 19

Researchers have found that eye color and risk of alcoholism are related. Jonathan Bassett and James Dabbs (2001) speculated that because light-eyed people are generally less responsive to drugs in general, they might drink more alcohol before they felt its effects. This increased exposure might make light-eyed people more likely to become dependent on alcohol. So, they examined a very large "archival" sample-a set of records that been collected in previous research-and looked at this "old" data in a new way. First, they went to the records of the Georgia Board of Pardons and Paroles and looked at the data on eye color and history of problems with alcohol abuse for a set of Caucasian male inmates of the Georgia Prison System. They separated the sample into two groups: "light-eyed" (blue, gray, green, and hazel eyes) and "dark-eyed" (brown and black eyes). They then counted the number of inmates in each group who had been identified in the prison records as having a history of problems with alcohol. The data in Table 3.20 are representative of what they found. Use the data to answer the questions that follow.
$$
\begin{array}{l|c|c|c}
\hline \text { History of Alcohol Abuse Problems } & \text { Light-colored Eyes } & \text { Dark-colored Eyes } & \text { Row Totals } \\
\hline \text { With } & 2,633 & 1,797 & \\
\hline \text { Without } & 3,637 & 2,933 & \\
\hline \text { Column totals } & & & \\
\hline
\end{array}
$$
a. Why did Bassett and Dabbs look at the records of only Caucasian inmates?
b. How many inmate records, in total, were examined?
c. How many inmates with light-colored eyes were in the sample?
d. How many inmates with dark-colored eyes were in the sample?
e. How many inmates had a history of alcohol abuse?
f. Construct two pie charts, one for each group (light-eyed and dark-eyed), showing the
percentage of inmates in each group with and without a history of alcohol abuse.
g. Is there evidence of a relationship between eye color and alcohol dependency?

Jon Southam
Jon Southam
Numerade Educator
02:42

Problem 20

. Let’s stick with Bassett and Dabbs (2001) for a moment. They also examined archival
records from the Bureau of Labor Statistics (collected in 1979) and wondered if women
with light-colored eyes consumed more alcohol overall than did women with darkcolored eyes. The data in Table 3.21 are representative of the results these authors found.
a. Use the data in the table to construct a bar graph displaying the mean number of
drinks consumed “last week” for light- and dark-eyed women in this sample.
b. Graph the mean number of drinks consumed in the previous month for both groups.
c. Graph the mean number of days in the previous month for which the women
reported drinking more than six drinks in that 24-hour period.
d. In your opinion, is it easier to understand the data when presented as numbers in a
table or when presented graphically?
$$
\begin{array}{l|c|c}
& \text { Light-eyed } & \text { Dark-eyed } \\
\hline \text { Mean number of drinks last week } & 1.39 & 1.29 \\
\hline \text { Mean number of drinks last month } & 5.78 & 4.91 \\
\hline \text { Mean number of days in last month drank more than 6 drinks } & 1.02 & 0.75 \\
\hline
\end{array}
$$

Nick Johnson
Nick Johnson
Numerade Educator
07:10

Problem 21

All of the data collected by Bassett and Dabbs (2001) were archival. Consider this
method for collecting data as you answer the following questions:
a. Do you see any problems with using archival data? Would it be better to go directly
to the source and collect data via interview or questionnaire from people today
rather than to rely on data from the archives?
b. The data in the second study regarding number of drinks consumed were obtained
via “self-report.” The women were asked about their drinking habits, and they then
wrote their answers down. Do you see any problems with this method of data collection? Should the data, graphic or numeric, be looked at with suspicion or caution
because of the way the data were collected?

Alex Loukas
Alex Loukas
Numerade Educator
02:14

Problem 22

The Morbidity and Mortality Weekly Report (MMWR) from the Centers for Disease Control
and Prevention describes an unexplained acute neurological illness that has been affecting
young children in the Muzaffarpur district of Bihar state in India. Reports of this strange,
and unfortunately often fatal, illness began in 1995 and continue to this day. In an effort to
determine the cause of this disorder, researchers at the CDC began tracking the rates of admission for this disease across the course of a year. Figure 3.11 comes from the MMWR for
January 30, 2015 (Shrivastava et al., 2015). Use the graph to answer the following questions:
a. Is there a relationship between number of patients admitted with symptoms of this
illness and month? What does the relationship look like?
b. Is there a relationship between the number of deaths from this illness and time of year?
c. Speculate about why rates of admission and time of year might be related. Is there something happening in June in India that might be related to outbreaks of this illness?

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
02:00

Problem 23

In the mid-1800s, John Snow, now considered the “Father of Epidemiology,” studied
a deadly outbreak of cholera. At the time, cholera was thought to be caused by “bad
air”—apparently, London smelled bad and doctors thought this bad smell caused disease. Snow suspected there might be another cause, and he was determined to find it in
order to prevent the disease from occurring in the future. He created a new kind of graph
to see if cholera might be caused by something in the public water supply, which was provided to neighborhoods in London by a series of public pumps. Snow focused on the
neighborhood where the outbreak started and watched the behavior of the women in the
neighborhood, paying attention to the specific pump where most households got their
water for the day. Snow then marked each residence on a map of the neighborhood and
indicated the number of deaths in that building with a dot—one dot for each death in a
given house. Mark Monmonier is one of many cartographers who have redrawn Snow’s
resulting graph (now called a “spot map”) to show how cases of illness are distributed
across a given region. His version is presented below in Figure 3.12.
a. Is there a relationship between the Broad Street Pump and deaths from cholera?
b. What aspects of Snow’s spot map led you to your conclusion?

Lara Gossage
Lara Gossage
Numerade Educator
01:55

Problem 24

After collecting the data on pump usage and deaths from cholera, Snow decided that the
problem was localized to one specific pump: the one on Broad Street, at the center of the
outbreak. It took some effort to convince the powers-that-be, but eventually, Snow got
permission to shut the pump down. On September 8, 1854, Snow had the handle removed from the Broad Street pump. Figure 3.13 is a graph created by Edward Tufte to show the
number of deaths from cholera before and after the Broad Street pump was disabled.
a. Did removal of the pump handle work?
b. Is the change in number of deaths after removal of the pump handle enough for you
(or Mr. Snow) to conclude that cholera is caused by something in the water?
c. What would you do next in your hunt for the cause of this disease?

Edward Adams
Edward Adams
Numerade Educator
04:43

Problem 25

. Complete the crossword puzzle shown below.
ACROSS
3. Observations between adjacent points
not possible
5. First person to use graphs to illustrate
data
9. (2 words) Graph best suited to show
relative frequency
10. (2 words) Bars touch on this graph
DOWN
1. Vertical axis on a graph
2. (2 words) Bars do not touch on this
graph
4. Observations between adjacent points
are possible
6. (2 words) Graph showing change in a
quantitative variable over time
7. Observation in the “one’s” place
8. Horizontal axis on a graph
11. Graph showing relationship between
two variables

Karen Burcham
Karen Burcham
Numerade Educator