More Spread The data set on the left represents the annual rate of return (in percent)

Chapter 3, Problem 45

(choose chapter or problem)

More Spread? The data set on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds (a) Determine the mean and standard deviation of each data set.(b) Based only on the standard deviation, which data set hasmore spread?(c) What proportion of the observations is within one standarddeviation of the mean for each data set?(d) The coefficient of variation, CV, is defined as the ratio of thestandard deviation to the mean of a data set, soCV = standard deviationmeanThe coefficient of variation is unitless and allows forcomparison in spread between two data sets by describingthe amount of spread per unit mean. After all, larger numberswill likely have a larger standard deviation simply due to thesize of the numbers. Compute the coefficient of variationfor both data sets. Which data set do you believe has morespread?(e) Lets take this idea one step further. The following datarepresent the height of a random sample of 8 male college students. The data set on the left has their height measured ininches, and the data set on the right has their height measuredin centimeters. For each data set, determine the mean and the standarddeviation. Would you say that the height of the males is moredispersed based on the standard deviation of height measuredin centimeters? Why? Now, determine the coefficient ofvariation for each data set. What did you find?