Deck 3: Numerical Methods for Describing Data Distributions

Question 1

The interquartile range is resistant to the effect of outliers.

Answer 1

True

Question 2

By definition, a data point is an outlier if it is mo re than 3.0 iqr away from
the closest quartile.

Answer 2

False

Question 3

Multiple sclerosis (MS) is an autoimmune disease that affects the brain and spinal cord.
MS affects women more than men, and is most commonly diagnosed between the ages of
20 and 40. MS sufferers typically have problems of coordination and walking. The
standard care for some sufferers is a plastic device affixed to the lower leg and ankle. In
a recent test of this device, volunteers with MS were randomly assigned to two
experimental groups. The volunteers in one group used the plastic device; the volunteers
in the other group did not use the plastic device. Each individual was timed as he or she
climbed a set of stairs. Times, measured without the device (ND) and with the device
(D), are presented below.
Using appropriate statistical terminology, compare the center, shape, and spread of
times on the stair-climbing with and without the device.

Answer 3

The centers of the distributions are similar, and both distributions are skewed to the
right with similar variabilities.

Question 4

For any given data set, the median must be greater than or equal to the
lower quartile, and less than or equal to the upper quartile.

Question 5

Multiple sclerosis (MS) is an autoimmune disease that affects the brain and spinal cord.
MS affects women more than men, and is most commonly diagnosed between the ages of
20 and 40. MS sufferers typically have problems of coordination and walking. The
standard care for some sufferers is a plastic device affixed to the lower leg and ankle. In
a recent test of this device, volunteers with MS were randomly assigned to two
experimental groups. The volunteers in one group used the plastic device; the volunteers
in the other group did not use the plastic device. Each individual was timed as he or she
climbed a set of stairs. Times, measured without the device (ND) and with the device
(D), are presented below.
Does it appear from your graphs above that the device helps the MS sufferers in the
stair-climbing test? Explain your reasoning in a few sentences.

Question 6

Deviations from the mean are always positive.

Question 7

Construct a back-to-back stem-and-leaf display that will allow comparison of the
times on the walking task.

Question 8

Multiple sclerosis (MS) is an autoimmune disease that affects the brain and spinal cord.
MS affects women more than men, and is most commonly diagnosed between the ages of
20 and 40. MS sufferers typically have problems of coordination and walking. The
standard care for some sufferers is a plastic device affixed to the lower leg and ankle. In
a recent test of this device, volunteers with MS were randomly assigned to two
experimental groups. The volunteers in one group used the plastic device; the volunteers
in the other group did not use the plastic device. Each individual was timed as he or she
climbed a set of stairs. Times, measured without the device (ND) and with the device
(D), are presented below.
Calculate the values of these numerical summaries for the stair-climbing task without
the device: Note: The table above is reproduced below so that you need not flip back and forth.

Question 9

Calculate the values of these numerical summaries for the walking task without the
device:

Question 10

the coins minted in Rome. Some of the summary statistics
are given in the table on the right.
(a) Describe a procedure that uses some or all o f these
summary statistics to determine whether outliers are

Question 11

Multiple sclerosis (MS) is an autoimmune disease that affects the brain and spinal cord.
MS affects women more than men, and is most commonly diagnosed between the ages of
20 and 40. MS sufferers typically have problems of coordination and walking. The
standard care for some sufferers is a plastic device affixed to the lower leg and ankle. In
a recent test of this device, volunteers with MS were randomly assigned to two
experimental groups. The volunteers in one group used the plastic device; the volunteers
in the other group did not use the plastic device. Each individual was timed as he or she
climbed a set of stairs. Times, measured without the device (ND) and with the device
(D), are presented below.
Construct a back-to-back stem-and-leaf display that will allow comparison of the
times on the stair-climbing task.

Question 12

One disadvantage of using the mean as a measure of center for a data set is
that its value can be affected by the presence of even a single outlier in the
data set.

Question 13

The mean is the middle value of an ordered data set.

Question 14

If there are no outliers, a boxplot and modified boxplot can differ in the
length of the box, but not in the whisker lengths.

Question 15

The interquartile range is a measure of spread in a set of data.

Question 16

Using appropriate statistical terminology, compare the center, shape, and spread of
times on the walking task with and without the device.

Question 17

Does it appear from your graphs above that the device helps the MS sufferers in the
walking test? Explain your reasoning in a few sentences.

Question 18

Approximately 68% of observations are within 2 standard deviations of
the mean if the distribution is approximately normal.

Question 19

The variance is the positive square root of the standard deviation.

Question 20

s is a measure of the variability of a population.

Question 21

Higher vertebrates (mammals and birds) exhibit lateralized behaviors, commonly referred
to as "handedness." Recently an investigator studied the coiling behavior of the
Agkistrodon piscivorus leucostoma - more commonly known as the cottonmouth snake.
The cottonmouth is a venomous snake that spends much of its time in a coil, sometimes
coiled in a counter-clockwise direction, other times in a clockwise direction. The
investigator made many observations of coiling behavior, and calculated a "laterality
index" for 30 cottonmouths. He defined the laterality index for each snake as the
percentage of observations of the snake that were categorized as coils in the counter-
clockwise direction. In the table below the data on laterality has been separated into two
groups: females and males.
Using your box plots from part (a), compare the distributions of laterality index for
males and females. Justify your comparisons by appealing to specific aspects of the
box plots constructed in Question 2.

Question 22

The forces that determine the size of groups ("swarms") of social insects and the rates at
which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis,
investigators dismantled a nest of these insects and marked a few insects for future
identification in new swarms. Twenty-five days after dismantling the original swarm they
had located new swarms of wasps from the original colonies. The data below present the
numbers of adults and workers in the new swarms in two different years. "Drones" are
fertile males that mate with the queen. "Workers" are infertile females that labor in the nest
and defend the colony.

Question 23

The forces that determine the size of groups ("swarms") of social insects and the rates at
which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis,
investigators dismantled a nest of these insects and marked a few insects for future
identification in new swarms. Twenty-five days after dismantling the original swarm they
had located new swarms of wasps from the original colonies. The data below present the
numbers of adults and workers in the new swarms in two different years. "Drones" are
fertile males that mate with the queen. "Workers" are infertile females that labor in the nest
and defend the colony.
(a) Approximately what percent of palate widths in this sample exceed 2.9 cm?
(b) What is the approximate percentile of a palate width that is 2.0 cm?

Question 24

3 (a) What is the approximate diameter of a hickory tree at the 20th percentile in this
distribution?
(b) According to the Empirical Rule, approximately 68% of hickory tree diameters
are between what two values?

Question 25

(a) What is the approximate diameter of an ash tree at the 20th percentile in this
distribution?
(b) According to the Empirical Rule, approximately 68% of ash tree diameters are
between what two values?

Question 26

The forces that determine the size of groups ("swarms") of social insects and the rates at
which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis,
investigators dismantled a nest of these insects and marked a few insects for future
identification in new swarms. Twenty-five days after dismantling the original swarm they
had located new swarms of wasps from the original colonies. The data below present the
numbers of adults and workers in the new swarms in two different years. "Drones" are
fertile males that mate with the queen. "Workers" are infertile females that labor in the nest
and defend the colony.
Using your box plots from part (a), compare the distributions of first and second year
drones. Justify your comparisons by appealing to specific aspects of the box plots
constructed in Question 2.

Question 27

Higher vertebrates (mammals and birds) exhibit lateralized behaviors, commonly referred
to as "handedness." Recently an investigator studied the coiling behavior of the
Agkistrodon piscivorus leucostoma - more commonly known as the cottonmouth snake.
The cottonmouth is a venomous snake that spends much of its time in a coil, sometimes
coiled in a counter-clockwise direction, other times in a clockwise direction. The
investigator made many observations of coiling behavior, and calculated a "laterality
index" for 30 cottonmouths. He defined the laterality index for each snake as the
percentage of observations of the snake that were categorized as coils in the counter-
clockwise direction. In the table below the data on laterality has been separated into two
groups: females and males.

Question 28

Higher vertebrates (mammals and birds) exhibit lateralized behaviors, commonly referred
to as "handedness." Recently an investigator studied the coiling behavior of the
Agkistrodon piscivorus leucostoma - more commonly known as the cottonmouth snake.
The cottonmouth is a venomous snake that spends much of its time in a coil, sometimes
coiled in a counter-clockwise direction, other times in a clockwise direction. The
investigator made many observations of coiling behavior, and calculated a "laterality
index" for 30 cottonmouths. He defined the laterality index for each snake as the
percentage of observations of the snake that were categorized as coils in the counter-
clockwise direction. In the table below the data on laterality has been separated into two
groups: females and males.
Construct comparative box plots of the laterality indices of female and male
cottonmouths.

Question 29

The forces that determine the size of groups ("swarms") of social insects and the rates at
which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis,
investigators dismantled a nest of these insects and marked a few insects for future
identification in new swarms. Twenty-five days after dismantling the original swarm they
had located new swarms of wasps from the original colonies. The data below present the
numbers of adults and workers in the new swarms in two different years. "Drones" are
fertile males that mate with the queen. "Workers" are infertile females that labor in the nest
and defend the colony.
Construct comparative box plots of the numbers of drones in the swarms in the
first and second years.

Question 30

The % by weight of the element Lead was also calculated for present in the data.
(b) Using your procedure from part (a), determine if there are outliers in these data.

Question 31

Higher vertebrates (mammals and birds) exhibit lateralized behaviors, commonly referred
to as "handedness." Recently an investigator studied the coiling behavior of the
Agkistrodon piscivorus leucostoma - more commonly known as the cottonmouth snake.
The cottonmouth is a venomous snake that spends much of its time in a coil, sometimes
coiled in a counter-clockwise direction, other times in a clockwise direction. The
investigator made many observations of coiling behavior, and calculated a "laterality
index" for 30 cottonmouths. He defined the laterality index for each snake as the
percentage of observations of the snake that were categorized as coils in the counter-
clockwise direction. In the table below the data on laterality has been separated into two
groups: females and males.
Calculate the values of these numerical summaries for the laterality index for the
sample of male cottonmouths: The table below presents some summary statistics from the distribution of laterality index
of males and females.

Question 32