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1) Compare the %Daily Value for Total Fat(g) to the %Daily Value for Saturated Fat(g) for these McDonald's® sandwiches.
a) Calculate the five number summary for both %Daily Values.
b) Construct parallel box plots for both.
c) Make at least four observations to compare these two distributions.
Source: http://nutrition.mcdonalds.com. July 27, 2011.
2) The heights of the students in a statistics class were all measured to the nearest inch. The results are presented in this back-to-back stem plot. Notice that it is also a split stem plot. The girls' heights are ordered out to the right on the right side. And the boys' heights are ordered out to the left on the left side.
a) Compute the standard deviation, the range, and the IQR for both girls and boys.
b) Compare the spread for the two groups, based on your answers to (a), in context.
c) Compute the mean, median, and mode for both boys and girls.
d) Compare the center for the two groups, based on your answers to (c), in context.
e) Compare the shape of the distributions, based on the graph, in context.
3) Compare the results of the Probability and Statistics District Common Assessment for two statistics classes.
a) Construct back-to-back stem plots (use split-stems) for these two classes.
b) Calculate the five number summaries for both classes.
c) Calculate the following statistics for both classes: mean, standard deviation, mode, range, and IQR.
d) Compare and contrast the two distributions. This should be in context and you should make at least four distinct observations.
4) The number of home-runs during a season is one of the statistics recorded about baseball players. The following table has the number of home-runs (over many seasons) for several of the best hitters in baseball. Compare the home-run hitting performance of these exceptional baseball players.
a) Calculate the following statistics for all four players:
= ____ sx= _____ IQR = _____ 5 # summary = {__, __, ___, ___, ___}
b) Construct Parallel Box Plots for the four players. Be sure to use the same scale for all four graphs and to label each graph.
c) Test for outliers, for all four players, using the 1.5*IQR criterion-(show work).
d) Compare and contrast the four distributions. This should be in context and you should make at least four distinct observations.
5) The following box plots show the average miles per gallon (city) for various types of vehicles. Comment on what these parallel box plots show. This should be in context and include at least 4 distinct observations. The dots represent outliers for that data set.
boxplot(MPG.city~Type) # base package
6) Refer to the four dot plots to answer the questions that follow.
Graph I
Graph II
Graph III
Graph IV
a) Identify the overall shape of each distribution.
b) How would you characterize the center(s) of these distributions?
c) Name at least two statistics that would most likely be the same for all four of these distributions.
d) Which of these distributions has the smallest standard deviation? Which of these distributions has the largest standard deviation? Explain.
e) For which of these distributions would it be appropriate to use the mean and standard deviation as numerical summaries? For which would the five number summary be more appropriate?
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