When studying phenomena such as inflation or population changes that involve periodic increases or decreases, the geometric mean is used to find the average change over the entire period under study. To calculate the geometric mean of a sequence of n values x1, x2,..., xn, we multiply them together and then find the nth root of this product. Thus
Suppose that the inflation rates for the last five years are 4%, 3%, 5%, 6%, and 8%, respectively. Thus at the end of the first year, the price index will be 1.04 times the price index at the beginning of the year, and so on. Find the mean rate of inflation over the 5-year period by finding the geometric mean of the data set 1.04, 1.03, 1.05, 1.06, and 1.08. (Hint: Here, n = 5, x1 = 1.04 = x2 = 1.03, and so on. Use the x1/n key on your calculator to find the fifth root. The mean inflation rate will be obtained by subtracting 1 from the geometric mean.)
Answer to relevant QuestionsThe range, as a measure of spread, has the disadvantage of being influenced by outliers. Illustrate this with an example. The following data set belongs to a sample: Calculate the range, variance, and standard deviation. Refer to Exercise 3.24, which listed the number of women from each of 12 countries who were on the Rolex Women’s World Golf Rankings Top 50 list as of July 18, 2011. Those data are reproduced here: Calculate the range, ...One disadvantage of the standard deviation as a measure of dispersion is that it is a measure of absolute variability and not of relative variability. Sometimes we may need to compare the variability of two different data ...The following table gives the frequency distribution of the number of hours spent last week on cell phones (making phone calls and texting) by all 100 students of the tenth grade at a school. Hours per Week Number ...
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