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.

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.

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.)

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.

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.

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.

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?

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.

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.

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.)

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.

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.)

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.)

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.

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.

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.