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Chapter 1: Q 99. (page 76)
Foot lengths Here are the foot lengths (in centimeters) for a random sample of seven 14-year-olds from the United Kingdom:
Calculate the standard deviation. Interpret this value.
The standard deviation is 2.5166 cm.
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U.S. women鈥檚 soccer鈥�2016 Earlier, we examined data on the number of goals scored by the 2016 U.S. women鈥檚 soccer team in 20 games played. The following dotplot displays the goal differential for those same games, computed as U.S. goals scored minus opponent goals scored.
Part (a). Explain what the dot above 3 represents.
Part (b). What does the graph tell us about how well the team did in 2016? Be specific.
The histogram shows the distribution of the percent of women aged 15 and over who have never married in each of the 50 states and the District of Columbia. Which of the following statements about the histogram is correct?
a. The center (median) of the distribution is about 36%.
b. There are more states with percentages above 32 than there are states with percentages less than 24.
c. It would be better if the values from 34 to 50 were deleted on the horizontal axis so there wouldn鈥檛 be a large gap.
d. There was one state with a value of exactly 33%.
e. About half of the states had percentages between 24% and 28%.
Watch that caffeine! The U.S. Food and Drug Adminis tration (USFDA) limits the amount of caffeine in a 12-ounce can of carbonated beverage to 72 milligrams. That translates to a maximum of 48 milligrams of caffeine per 8-ounce serving. Data on the caffeine content of popular soft drinks (in milligrams per 8-ounce serving) are displayed in the stemplot.
Part (a). Why did we split stems?
Part (b). Give an appropriate key for this graph.
Part (c). Describe the shape of the distribution. Are there any outliers?
A class survey Here is a small part of the data set that describes the students in an AP庐 Statistics class. The data come from anonymous responses to a questionnaire filled out on the first day of class.
(a) Identify the individuals in this data set.
(b) What are the variables? Classify each as categorical or quantitative.
Simpson鈥檚 paradoxAccident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save time. Do they also save lives? The two-way table summarizes data from a sample of patients who were transported to the hospital by helicopter or by ambulance.
(a) What percent of patients died with each method of transport? Here are the same data broken down by severity of accident:
(b) Calculate the percent of patients who died with each method of transport for the serious accidents. Then calculate the percent of patients who died with each method of transport for the less serious accidents. What do you notice?
(c) See if you can explain how the result in part (a) is possible given the result in part (b).
Note: This is an example of Simpson鈥檚 paradox, which states that an association between two variables that holds for each value of a third variable can be changed or even reversed when the data for all values of the third variable are combined.
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