Deck 3: Numerical Methods for

Question 1

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

Answer 1

False

Question 2

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 thestair-climbing test?
Explain your reasoning in a few sentences.

Answer 2

From the graph, it appears that the device does help MS sufferers in the stair-climbing test. The average time taken to climb the stairs without the device (ND) is noticeably higher than the average time taken with the device (D). This suggests that the device improves the ability of MS sufferers to climb stairs, as it likely provides better coordination and stability. Additionally, the range of times for the group using the device is narrower, indicating more consistent performance, while the range for the group not using the device is wider, suggesting more variability in performance. Overall, the data supports the conclusion that the plastic device is beneficial for MS sufferers in the stair-climbing test.

Question 3

Deviations from the mean are always positive.

Answer 3

False

Question 4

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 withoutthe device: Note: The table above is reproduced below so that you need not flip back and forth.

Question 5

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

Question 6

The measurements in the table at right are from coins mintedthat different mints reveal themselves in different traceelement profiles in the coins. Atomic AbsorptionSpectrometry was used to estimate the % by weight of gold;these data are presented here.
(a) Construct a box plot for these data.in Rome during first three centuries AD. Historians believe
(b) Would you say this distribution is skewed or approximately symmetric?
Justifyyour response using appropriate statistical terminology.

Question 7

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

Question 8

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

Question 9

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

Question 10

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 timed as they walked across a room.
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 thewalking test?
Explain your reasoning in a few sentences.

Question 11

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

Question 12

s is a measure of the variability of a population.

Question 13

The interquartile range is resistant to the effect of outliers.

Question 14

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

Question 15

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 timed as they walked across a room.
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 thetimes on the walking task.

Question 16

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 thetimes on the stair-climbing task.

Question 17

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

Question 18

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 oftimes on the stair-climbing with and without the device.

Question 19

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 timed as they walked across a room.
Times, measured without the device (ND) and with the device (D), are presented below.


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

Question 20

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 timed as they walked across a room.
Times, measured without the device (ND) and with the device (D), are presented below.



-Calculate the values of these numerical summaries for the walking task without thedevice:a) The mean __________________b) The standard deviation ___________________c) The median ___________________d) The interquartile range ___________________

Question 21

Grey Kangaroos are large social marsupials, indigenous to Australia. As part of astudy of these creatures, biologists measured various aspects of their skeletalstructure. A sample of 148 palate widths is presented in the stem-and-leaf plot below.The display uses five lines for each stem. Thus, "2t|" is the stem for palate widths of22 and 23, "2f|" for 24 and 25, "2s|" for 26 and 27, and so on. (The "t" then stands forleaves that are twos and threes, the "f" for leaves of fours and fives, etc. "2."Indicates leaves that are zeros and ones; "2*" indicates leaves that are eights andnines.) The mean palate width of this sample is 2.6 cm, and the standard deviation is 0.3 cm. (a) Approximately what percent of palate widths in this sample are less than 2.9 cm?
(b) What is the approximate percentile of a palate width that is 2.0 cm?

Question 22

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 counterclockwise direction.

-Using your box plots , compare the distributions of laterality index formales and females. Justify your comparisons by appealing to specific aspects of thebox plots constructed in https://storage.examlex.com/TB5309/.

Question 23

Grey Kangaroos are large social marsupials, indigenous to Australia. As part of astudy of these creatures, biologists measured various aspects of their skeletalstructure. Data on palate width from a sample of 124 grey kangaroos are presented inthe stem-and-leaf display below. The display uses five lines for each stem. Thus,"2t|" is the stem for palate widths of 22 and 23, "2f|" for 24 and 25, "2s|" for 26 and27, and so on. (The "t" then stands for leaves that are twos and threes, the "f" forleaves of fours and fives, etc. "2." Indicates leaves that are zeros and ones; "2*"indicates leaves that are eights and nines.)The mean palate width of this sample is 2.6cm, and the standard deviation is 0.3 cm. (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

The % by weight of the element Lead was also calculated forare given in the table on the right.
(a) Describe a procedure that uses some or all o f thesesummary statistics to determine whether outliers arepresent in the data.the coins minted in Rome. Some of the summary statistics
(b) Using your procedure from part (a), determine if there are outliers in these data.

Question 25

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.

-Using your box plots , compare the distributions of first and second yeardrones. Justify your comparisons by appealing to specific aspects of the box plotsconstructed in

Question 26

The table below presents some summary statistics from the distribution of laterality index of males and females


-Construct comparative box plots of the laterality indices of female and malecottonmouths.Male

Question 27

Engineers initially surveyed the Territory of Iowa in the 1830's, and they were verycareful to take note of the trees and vegetation. The sample of Ash tree diametersfrom the original survey o f what is now Linn County is presented in the stem-and-leafdisplay below. The display uses five lines for each stem. Thus, "1t|" is the stem fordiameters of 12 and 13, "1f|" for 14 and 15, "1s|" for 16 and 17, and so on. (The "t"then stands for leaves that are twos and threes, the "f" for leaves of fours and fives,etc.)The mean diameter of the 102 ash trees in this sample is 11.500 inches, and thestandard deviation is 3.842 inches.
(a) What is the approximate diameter of an ash tree at the 20th percentile in thisdistribution?

(b) According to the Empirical Rule, approximately 68% of ash tree diameters arebetween what two values?

Question 28

A wide variety of oak trees grow in the United States. In onelocations, and their volumes, in m3, were recorded. The tableat right presents summary statistics for these data.
(a) Describe a procedure that uses some or all of thesestudy, a sample of acorns was collected from different
summary statistics to determine whether outliers arepresent in the data.
(b) Using your procedure from part (a), determine if there are outliers in these data.

Question 29

The table below presents some summary statistics from the distributions of the number of drones.



-Construct comparative box plots of the numbers of drones in the swarms in thefirst and second years.

Question 30

Engineers initially surveyed the Territory of Iowa in the 1830's, and they were verycareful to take note of the trees and vegetation. The sample of hickory tree diametersfrom the original survey of what is now Linn County, is presented in the stem andleaf plot below. The display uses five lines for each stem. Thus, "1t|" is the stem fordiameters of 12 and 13, "1f|" for 14 and 15, "1s|" for 16 and 17, and so on. (The "t"then stands for leaves that are twos and threes, the "f" for leaves of fours and fives,etc.)The mean diameter of the 73 hickory trees in this sample is 11.849 inches, and thestandard deviation is 3.995 inches.
(a) What is the approximate diameter of a hickory tree at the 20th percentile in thisdistribution?

(b) According to the Empirical Rule, approximately 68% of hickory tree diametersare between what two values?

Question 31

The Economist is a weekly newspaper that focuses onyear the "Big Mac Index," the price ($ U. S.) of a BigMac in countries around the world, is published as alight-hearted way of comparing currencies. The valuesfor 19 countries are displayed at right. ($3.41 was theU.S. price at publication in the summer of 2007.)international politics, business news, and opinion. Each
(a) Construct a box plot for these data.
(b) Would you say this distribution is skewed or approximately symmetric?
Justifyyour response using appropriate statistical terminology.