# 0.5 - Practice problems

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At the end of each chapter, there is a section filled with questions related to the material. Your instructor has a file that contains the R code required to provide the results to answer all these questions. To practice learning R, it would be most useful for you to try to accomplish the requested tasks first yourself in R and then refer to the provided R code when you struggle. These questions provide a great venue to check what you are learning, see the methods applied to another data set, and to discuss in study groups, with your instructor, or at the Math Learning Center, especially if you have any questions about the correct responses.

0.1. Read in the treadmill data set discussed above and find the mean and SD of the Ages (*Age variable*) and Body Weights (*BodyWeight*). In studies involving human subjects, it is common to report a summaries of characteristics of the subjects. Why does this matter? Think about how your interpretation of any study of the fitness of subjects would change if the mean age had been 20 years older or 35 years younger.

0.2. How does knowing about the distribution of results for *Age* and *BodyWeight* help you understand the results for the Run Times discussed above?

0.3. The mean and SD are most useful as summary statistics only if the distribution is relatively symmetric. Make a histogram of *Age* responses and discuss the shape of the distribution (is it skewed right, skewed left, approximately symmetric?; are there outliers?). Approximately what range of ages does this study pertain to?

0.4. The weight responses are in kilograms and you might prefer to see them in pounds. The conversion is lbs=2.205*kgs. Create a new variable in the treadmill data.frame called *BWlb* using this code:

treadmill$BWlb <- 2.205*treadmill$BodyWeight

and find the mean and SD of the new variable.

0.5. Make histograms and boxplots of the original *BodyWeight* and new *BWlb* variables. Discuss aspects of the distributions that changed and those that remained the same with the transformation from kilograms to pounds.