Histograms of the 2010 populations (in millions) and the numbers of seats in the House of Representatives, both by state, are shown in Fig. 42.

a. The 435 seats in the House of Representatives are divided up among the 50 states on the basis of the sizes of their populations as of the most recent census (in 2010). Why does it follow that the two histograms in Fig. 42 should have the same shape?
b. For each distribution, which is larger, the mean or the median? Explain.
c. The U.S. population was 308 million in 2010. Find the ratio of the 435 seats to the U.S. population (in millions). Round to the second decimal place. Use your result to find the number of representatives in Pennsylvania, whose 2010 population was 12.7 million.
d. The means of the population distribution and seat distribution are 6.16 million and 8.7 seats, respectively. Show that the mean state population (in millions) times the ratio you found in part (c) is approximately equal to the mean number of House seats in a state.
e. For the population distribution, the mean is 6.16 million and the median is 4.44 million. For the seat distribution, the mean is 8.7 seats and the median is 6 seats. Compute the ratio of the mean to the median for both the population distribution and the seat distribution. Round your results to the second decimal place. Explain why it makes sense that they are approximately equal.

Transcribed Image Text:

Population by State 25 5 20 15 10 10 20 Millions 30 40 House Seats by State 25 15 10 20 30 40 50 60 Seats