Census Data

The Bureau of the Census has the task of counting all of the people in the United States once every 10 years. It is a massive and costly enterprise involving an ever increasing staff of enumerators. The table below contains the population of the United States rounded to the nearest hundred thousands and the number of enumerator staff for the years 1790 to 1990. The data is from a Science News article1. Let x = 0 for the year 1790 and using a statistical package or a graphing calculator, make two scatterplots. The first scatterplot should have the number of years since 1790 as the independent variable and the population of the United States as the dependent variable. The second scatterplot should have the number of years since 1790 as the independent variable and the number of enumerator staff as the dependent variable. For each of these scatterplots, fit an equation of the form ln y = . . . . Discuss how well these equations fit the data.

A question has been raised about when the number of enumerator staff will equal the total population of the United States. Use the two equations that you fit to the scatterplots to determine the year in which this will happen. What will be the population of the United States in that year?

Year

Population of U.S.

# of enumerator staff

1790 3,900,000 650
1800 5,300,000 900
1810 7,200,000 1,100
1820 9,600,000 1,188
1830 12,900,000 1,519
1840 17,100,000 2,167
1850 23,200,000 3,231
1860 31,400,000 4,417
1870 38,600,000 6,530
1880 50,200,000 31,382
1890 63,000,000 46,804
1900 76,200,000 52,871
1910 92,200,000 70,266
1920 106,000,000 87,756
1930 123,200,000 87,756
1940 132,200,000 123,069
1950 151,300,000 142,962
1960 179,300,000 159,321
1970 203,200,000 166,408
1980 226,500,000 458,523
1990 248,700,000 510,200

Census Data

1Peterson, Ivars. "Census sampling confusion." Science News, Vol. 155, Number 10 (March 6, 1999).