The previous problem discusses GDP, which is a commonly used measure of the overall economic activity of a nation. For this group of nations, the GDP data have a mean of 1771 and a standard deviation of 2781 (in billions of U.S. dollars).
a. The five-number summary of GDP is minimum = 245, Q1 = 396, median = 731, Q3 = 2033, and maximum = 14,581. Sketch a box plot.
b. Based on your graph in part a, as well as the mean and standard deviation, describe the shape of the distribution of GDP values.
c. The data set also contains per capita GDP, or the overall GDP divided by the nation’s population size. Suppose we were to construct a scatterplot of per capita GDP and GDP. What trend might you expect to see?
d. Your friend, Joe, argues that the correlation between the two variables must be 1 since they are both measuring the same thing. In reality, the actual correlation between per capita GDP and GDP is only 0.247. Identify the flaw in Joe’s reasoning.