Exam 3: Numerical Summaries of Center and Variation

Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 14 car accidents; but there were actually 140 that day. How will this error affect the measures of center for this data?

The following boxplot contains information about the length of time (in minutes) it took women participants to finish the marathon race at the 2012 London Olympics.Use the plot for following questions -What can be said about the shape of the distribution of women's running times for the marathon?

Suppose we have the distribution of household income in the United States. What measures of center and spread would be best to describe this data?

Use the following information for following questions . The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. -95% of all people work between and hours per day?

Ten households were asked how many pets they currently own. The results are shown below. What is the IQR for this set of data?

Use the following information for following questions . The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours. -If Amanda slept 9.2 hours last night, would you consider this unusual?

The slowest 25% of men participants ran the marathon how quickly?

Approximately what value corresponds to the first quartile of the following boxplot?

A class of 20 history students took a quiz worth 100 points. The standard deviation of the scores was 0. What can you say about the scores of the students on this quiz?

Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 1500 car accidents; but there were actually only 150 that day. How will this error affect the measures of center for this data?

A class of 30 French students took a quiz worth 50 points. The standard deviation of the scores was 0. What must be true about the students' scores?

What feature of a distribution can NOT be determined from a boxplot?

The five-number summary of the ages of a group of 100 adults is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one adult whose age is a low outlier. (ii) There is at least one adult whose age is a high outlier.

The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from shortest to longest.

Use the following information for following questions A math professor has two routes he can take to campus. The length of time it takes to drive each of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation of 3 minutes. Assume that both distributions are unimodal and roughly symmetric. -Today, the z-score for the professor's travel time was −2.1. How many minutes did it take him to drive to campus if he took Route B?

The five-number summary of the length of phone calls of 100 people is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. Explain your reasoning. (i) There is at least one person made a phone call that is a low outlier. (ii) There is at least one person made a phone call that is a high outlier.

Use the following information for following questions A math professor has two routes he can take to campus. The length of time it takes to drive each of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation of 3 minutes. Assume that both distributions are unimodal and roughly symmetric. -If the professor takes Route A, how often will he be able to drive to campus between 16 and 24 minutes?

What is one feature of a distribution that can NOT be determined from a boxplot? The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics. Use the plot for Questions (19) and (20).

The mean can be thought of as the balancing point of a distribution.According to this description, at approximately what value is the following distribution balanced?