Question 1

What effect does adding ten points to every exam score in a class have on the interquartile range of the scores? Be specific and explain briefly.

Accepted Answer

Adding ten points to each score will have no effect on the interquartile range of the scores. Both the first and third quartile will have been raised by ten points, so the difference between them will be unchanged.

Question 2

In a study reported in the July 2007 issue of the Journal of Epidemiology and Community Health, researchers investigated whether veterans are more likely to commit suicide than nonveterans. They spent 12 years following 104,000 veterans who had served in the armed forces between 1917 and 1994, and compared them with 216,000 nonveterans. They found that 197 veterans and 311 nonveterans committed suicide.
-Describe and justify the conclusion that you would draw from this study.

Accepted Answer

This study indicates that veterans are about 1.3 times more likely than nonveterans to commit suicide. However, because this was an observational study, you cannot conclude that there is a causal relationship between serving in the armed forces and committing suicide.

Question 3

For each of the following, indicate whether it is resistant to outliers or not. Do not bother to explain your answers, except for the last one.
a. Mean
b. Median
c. Standard deviation
d. (Lower quartile + upper quartile) $/ 2$
e. $($ Maximum + minimum $) / 2$
f. Mean absolute deviation (Explain your answer.)

Accepted Answer

a. No, the mean is not resistant.
b. Yes, the median is resistant.
c. No, the standard deviation is not resistant.
d. Yes, this is resistant (because the quartiles are resistant).
e. No, this is not resistant (because the minimum and maximum are not resistant).
f. No, the mean absolute deviation is not resistant. An extreme value would have a large absolute deviation and would influence the mean enough that many values could have large absolute deviations. This, in turn, would affect the mean absolute deviation considerably because the mean is not resistant to outliers.

Question 4

Create an example of five hypothetical exam scores (between 0 and 100 , with repeats allowed) with the property that $80 \%$ of the scores are less than the mean.

Accepted Answer

The answer of Create an example of five hypothetical exam...

Question 5

The following side-by-side stemplot displays the total number of points scored per Super Bowl football game for the first 41 Super Bowls (from 1967-2007), separated according to the first 20 games (19671986) and the next 21 games (1987-2007): 
-For each group, determine the five-number summary of these total points.

Accepted Answer

The answer of The following side-by-side stemplot displays the total...

Question 6

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women: 
-Is number of close friends a quantitative or categorical variable?

Accepted Answer

The answer of The following table reports counts of the...

Question 7

What effect does adding 10 points to every exam score in a class have upon the mean score? In other words, how would the new mean compare to the old mean?
Be as specific as possible.

Accepted Answer

The answer of What effect does adding 10 points to...

Question 8

The following histogram displays the magnitudes of the 614 earthquakes with Richter scale magnitude greater than 1.0 that occurred in the United States between March 25 and April 1, 2004: 
-Which histogram do you think displays the variable height? Justify your answer.

Accepted Answer

The answer of The following histogram displays the magnitudes of...

Question 9

The following histogram displays the magnitudes of the 614 earthquakes with Richter scale magnitude greater than 1.0 that occurred in the United States between March 25 and April 1, 2004: 
-Which histogram do you think displays the variable number of siblings? Justify your answer.

Accepted Answer

The answer of The following histogram displays the magnitudes of...

Question 10

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women: 
-Calculate the median number of close friends for each gender.

Accepted Answer

The answer of The following table reports counts of the...

Question 11

The following side-by-side stemplot displays the total number of points scored per Super Bowl football game for the first 41 Super Bowls (from 1967-2007), separated according to the first 20 games (19671986) and the next 21 games (1987-2007): 
-Does this stemplot enable you to determine how many points were scored in the first Super Bowl? If so, what is this number?

Accepted Answer

The answer of The following side-by-side stemplot displays the total...

Question 12

Would a manufacturer of candy bars want to have a larger standard deviation of the weights of candy bars coming off the assembly line or a small standard deviation of those weights? Explain briefly.

Accepted Answer

The answer of Would a manufacturer of candy bars want...

Question 13

The following histogram displays the life expectancies (in years), as reported by The World Almanac and Book of Facts 2006, for a sample of 22 countries:  
a. Describe (in five words or less) the shape of this distribution.
b. Two measures of center for this distribution are 67.0 and 70.7. One of these is the mean and the other is the median. Which is which? Explain your choice.
Now consider a histogram of the numbers of televisions per thousand people in these countries:  c. Write a paragraph describing key features of this distribution.

Accepted Answer

The answer of The following histogram displays the life expectancies...

Question 14

Construct a hypothetical example of ten exam scores (between 0 and 100 , inclusive, possibly including repeats) so that the interquartile range equals zero and the mean is greater than the median. (Both of these properties should hold for the example that you create.) Also report the values of the mean, median, and IQR for your example. (If you are unable to create an example for which both properties hold, then for partial credit try to create an example in which one of the properties holds.)

Accepted Answer

The answer of Construct a hypothetical example of ten exam...

Question 15

Create an example of five hypothetical exam scores (between 0 and 100, inclusive, with repeats allowed) with the property that the standard deviation is as small as possible.

Accepted Answer

The answer of Create an example of five hypothetical exam...

Question 16

In a recent study, researchers followed 104,000 U.S. veterans who had served in the armed forces and a comparison group of 216,000 nonveterans. Over a period of 12 years, they found that 197 veterans and 311 nonveterans committed suicide.
a. Calculate the relative risk of suicide, comparing veterans to nonveterans.
b. Write a sentence interpreting this relative risk value.
c. A segmented bar graph would not provide much helpful information for these data. Explain why not. (Do not bother to produce this graph.)

Accepted Answer

The answer of In a recent study, researchers followed 104,000...

Question 17

The following side-by-side stemplot displays the total number of points scored per Super Bowl football game for the first 41 Super Bowls (from 1967-2007), separated according to the first 20 games (19671986) and the next 21 games (1987-2007): 
-Construct boxplots of the distributions of total points in these two groups, using the same axes and scale. (Do not bother to check for outliers; there are no outliers in either distribution.)

Accepted Answer

The answer of The following side-by-side stemplot displays the total...

Question 18

Suppose Mary records the ages of people entering a McDonald's restaurant in a suburban shopping plaza tomorrow, while Abby records the ages of people entering a popular food court on a nearby college campus. Who would you expect to have the higher standard deviation of these ages: Mary (suburban McDonald's) or Abby (campus food court)? Explain briefly.

Accepted Answer

The answer of Suppose Mary records the ages of people...

Question 19

What effect does adding ten points to every exam score in a class have on the standard deviation of the scores? Be specific and explain briefly.

Accepted Answer

The answer of What effect does adding ten points to...

Question 20

In a recent study, researchers purchased 40 food items in New York City and determined the actual calorie content of each through a laboratory analysis. They then calculated the percentage difference between the actual calorie content and the calorie count listed on the item's label. (A positive percentage difference corresponds to a food item whose actual calorie content was higher than what the label claimed.) Each food item was also classified according to whether it was marketed locally, nationally, or regionally. The boxplots below were constructed to compare the distributions:  
Write a paragraph summarizing what these boxplots reveal about the percentage differences between measured and labeled calorie content among the three groups of food items.

Accepted Answer

The answer of In a recent study, researchers purchased 40...

Exam 2: Summarizing Data

What effect does adding ten points to every exam score in a class have on the interquartile range of the scores? Be specific and explain briefly.

Create an example of five hypothetical exam scores (between 0 and 100 , with repeats allowed) with the property that 80%80 \%80% of the scores are less than the mean.

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women: -Is number of close friends a quantitative or categorical variable?

What effect does adding 10 points to every exam score in a class have upon the mean score? In other words, how would the new mean compare to the old mean? Be as specific as possible.

The following histogram displays the magnitudes of the 614 earthquakes with Richter scale magnitude greater than 1.0 that occurred in the United States between March 25 and April 1, 2004: -Which histogram do you think displays the variable height? Justify your answer.

The following histogram displays the magnitudes of the 614 earthquakes with Richter scale magnitude greater than 1.0 that occurred in the United States between March 25 and April 1, 2004: -Which histogram do you think displays the variable number of siblings? Justify your answer.

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women: -Calculate the median number of close friends for each gender.

Would a manufacturer of candy bars want to have a larger standard deviation of the weights of candy bars coming off the assembly line or a small standard deviation of those weights? Explain briefly.

Create an example of five hypothetical exam scores (between 0 and 100, inclusive, with repeats allowed) with the property that the standard deviation is as small as possible.

What effect does adding ten points to every exam score in a class have on the standard deviation of the scores? Be specific and explain briefly.

Create an example of five hypothetical exam scores (between 0 and 100 , with repeats allowed) with the property that $80 \%$ of the scores are less than the mean.