Sociology 215: Demographic Methods

Spring 2002

Professor: S. Philip Morgan (pmorgan@soc.duke.edu)

 

Problem Set 1: Growth Rates

 

  1. The population size of the United States on 1 April 1980 was, according to the census of that date, 248,709,873. The census of 1 April 1990 and 2000 recorded _______________ and _______________ persons.

 

(Find answers at http://www.census.gov/)

 

A)    Suppose the growth rates were constant over the 1990-2000 interval: What would this growth rate be?

B)    At this rate, how long would it take the U.S. population to double in size?

C)    How many person-years were lived in the U.S. over the 1990-2000 period (again, assuming a constant growth rate)?

D)    What was the population size in 1995, the mid-point of the 1990-2000 period (again, assuming a constant growth rate)?

E)     If you estimated person-years as the population at the middle of the time period times the length of the interval, how (if at all) would this differ from the “true” number of person-years lived (again, assuming a constant growth rate)?

F)     Now suppose the growth rate varied during this interval: What was its mean value?

G)    If the growth rate were thought to have declined during this interval, how (if at all) would this affect the estimated number of person-years lived during the interval?

 

 

  1. The US. National Center for Health Statistics (NCHS http://www.cdc.gov/nchs/default.htm ) publishes the Vital Statistics Reports . Using Volume 50, No. 1 fill in the blanks below and then answer the questions that follow.

 

According to the U.S. National Center for Health Statistics, there were _______________ live birth in the 12 months ending with January 2000 and __________ live births in year ending January 2001.  The corresponding deaths were, respectively _________________ and ___________.  The Population bases for the 12-month period ending, respectively, with January 2000 and January 2001 were 273.1 million and 275.4 million (where the base is defined by NCHS as the estimated population at the midpoint of the period).

 

A)    What was the crude birth rate for the12 month period ending with Jan 2001?

B)     What was the crude death rate for the same interval?

C)    What was the crude rate of natural increase (same interval)?

D)    Determine the crude rate of net migration (same interval)?

E)     Determine the crude rate of in-migration (same interval)?

 

  1. According to the U.S. Bureau of the Census estimates, the population of the world on January 9, 2002 at 9:52:15 AM EST was 6,197,956,133. Three minutes and 4 seconds later (at 1/9/02 at 9:55:19 AM EST) the estimate is 6,197,956,581. (These estimates are available from the Census Bureau’s “dynamic clock”

 

A)    What was the growth rate over this interval?

B)     Is the growth rate that you calculated the crude growth rate, the instantaneous growth rate, the mean annual growth rate, or what?

C)    Given growth rate in this interval, when will the world population reach ten million? (The year is sufficient; I don’t need the month and day, much less the hour, minute and second!)

D)    What will be the world population size in the year 2020?