Follow these steps to find the equation for the median-median line for the data on life expectancy at birth for males in the United States for different years in the 20th century. Let x represent the year, and let y represent the male life expectancy in years.
Year of birth Male life-expectancy
(years)
1920 ......................... 53.6
1925 ......................... 56.3
1930 ......................... 58.1
1935 ......................... 59.4
1940 ......................... 60.8
1945 ......................... 62.8
1950 ......................... 65.6
1955 ......................... 66.2
1960 ......................... 66.6
1965 ......................... 66.8
1970 ......................... 67.1
1975 ......................... 68.8
1980 ......................... 70.0
1985 ......................... 71.2
1990 ......................... 71.8
1995 ......................... 72.5
1998 ......................... 73.9
a. How many points are there in each of the three groups?
b. What are the three representative points for these data? Graph these points.
c. Draw the line through the first and third points. What is the slope of this line? What is the real-world meaning of the slope?
d. Write the equation of the line through the first and third points. Rewrite this equation in intercept form.
e. Draw the line parallel to the line in 6d passing through the second point. What is the equation of this line? Rewrite this equation in intercept form.
f. Find the mean of the y-intercepts and write the equation of the median-median line. Graph this line. Remember to use the intercepts of all three lines.
g. The year 1978 is missing from the table. Using your model, what would you predict the life expectancy at birth to be for males born in 1978?
h. Use your model to predict the life expectancy at birth for males born in 1991.
i. Using this model, when would you predict the life expectancy at birth for males in the United States to exceed 80 years?