Exam 3: Numerical Methods for

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

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?

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.

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

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.

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

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.

The interquartile range is resistant to the effect of outliers.

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

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.

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.

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?

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.

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.

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.

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?

Deviations from the mean are always positive.

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.

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.

s is a measure of the variability of a population.