Drawing Comparative Inferences About Two Populations Using Measures of Variability

A random survey of seventh- and eighth-grade students was conducted to find out how many hours is spent doing homework each night. Of the two sets of data, which has the greater median?

• 7th Graders

• 8th Graders

• They have the same median.

• Impossible to determine from the box plot.

A random survey of seventh- and eighth-grade students was conducted to find out how many hours is spent doing homework each night. Which of the following conclusions may be made by comparing the interquartile ranges of each data set? Select all that apply.

• The interquartile range of both sets is equal to 1 hour.

• The interquartile range for eighth-graders is greater than the interquartile range for seventh-graders.

• The interquartile range for seventh-graders is greater than the interquartile range for eighth-graders.

• The data sets exhibit similar variability, or spread.

• The data for seventh-graders are more skewed than the data for eighth-graders.

Using the box plot, who spends more time in outdoor activity?

• Soccer players, because they have a greater range of active minutes outdoors.

• Basketball players, because they have a greater range of active minutes outdoors.

• Soccer players, because they have a greater median of minutes spent outdoors.

• Basketball players, because they have a greater median of minutes spent outdoors.

What can you infer about the athletes from the box plot?

• The data set for soccer players shows that they have less variability when compared to the data set for basketball players.

• The data set for soccer players shows that they have an equal amount of variability when compared to the data set for basketball players.

• The data set for soccer players shows that they have greater variability when compared to the data set for basketball players.

How can box-and-whisker plots be used to compare two sets of data? Select all that apply.

• They quickly illustrate measures of center.

• They identify all the data points in each data set.

• They show trends in data that can be compared.

• They display measures of variability for each data set.

• They easily show the mean of each data set.

Angela is comparing the amount of rainfall over the past month in two cities on days when it rained. In City​ 1, the range in rainfall is 4.5 centimeters and the interquartile range​ (IQR) is 1.5 centimeters. In City​ 2, the range is 5 centimeters and the IQR is 3 centimeters. What might you conclude about the cities based on the ranges and interquartile​ ranges?

• The rainfall amounts on days when it rains have the same variability for City 1 and City 2.

• The rainfall amounts on days when it rains have greater variability for City 2 than those for City 1.

• The rainfall amounts on days when it rains have greater variability for City 1 than those for City 2.

• The rainfall amounts on days when it rains are generally greater for City 2 than those for City 1.

The following box plots show the high​ temperatures, in degrees​ Fahrenheit, in two cities over the past 10 days. What might you conclude about the cities based on the interquartile​ ranges?

• The weather patterns in City 1 and City 2 are equally consistent.

• The weather pattern in City 1 is more consistent than the weather pattern in City 2.

• The weather pattern in City 2 is more consistent than the weather pattern in City 1.

The box plots show the distribution of times spent shopping by two different groups. Which of the following is a valid comparative inference?

• The median for Group A is higher, so they generally spend more time shopping.

• The interquartile range for Group A is higher, so they have a larger variability in shopping time.

• The range for Group B is higher, so they have a larger variability in shopping time.

• Both groups spend about the same amount of time shopping, in general.

The box plots show the distribution of times spent shopping by two different groups. Which group has a higher variability in the lower 50% of their data?

• Group A because their interquartile range is larger.

• Group B because their interquartile range is larger.

• Group A because the distance from their median to their maximum value is larger.

• Group B because the distance from their median to their maximum value is larger.