Beatles Outliers affect more than the statistics that measure the center of a distribution. Outliers also affect statistics that measure the spread of the distribution. Use the sizes of the songs in Exercise 55 for this exercise.
(a) Find the standard deviation and interquartile range of the sizes of the songs (in megabytes)
(b) Which of these summary statistics is most affected by the presence of the outlier? How do you know?
(c) Exclude the most extreme outlier from the data and find the mean and SD without this song. Which summary changes more when the outlier is excluded: the mean or SD?
Exercise 55
Beatles Outliers have a dramatic effect on small data sets. For this exercise, the data consist of the sizes (in seconds and MB) of the 27 #1 hits on the Beatles’ album 1.
(a) Generate the boxplot and histogram of the sizes of these songs.
(b) Identify any outliers. What is the size of this song, in minutes and megabytes?
(c) What is the effect of excluding this song on the mean and median of the sizes of the songs?
(d) Which summary, the mean or median, is the better summary of the center of the distribution of sizes?
(e) Which summary, the mean or median, is the more useful summary if you want to know if you can fit this album on your iPod?