The table below gives the educational attainment of the U.S. population 25 years and older
since 1960.
Males-
Percentage with 4 years of highschool
1960 39.5%
1970 51.9%
1980 67.3%
1990 77.7%
2000 84.2%
2004 84.8%
Percentage with 4 years of college or more
1960 9.7%
1970 13.5%
1980 20.1%
1990 24.4%
2000 27.8%
2004 29.4%
Females-
Percentage with 4 years of highschool or more
1960 42.5%
1970 52.8%
1980 65.8%
1990 77.5%
2000 84.0%
2004 85.4%
Percentage with 4 years of college or more
1960 5.8%
1970 8.1%
1980 12.8%
1990 18.4%
2000 23.6%
2004 26.1%
a) Write a matrix for the educational attainment of males
b) Write a matrix for the educational attainment of females
c)Use the matrices from parts a and b to write a matrix showing the difference in educational
attainment between males and females since 1960
a) The matrix for the educational attainment of males can be written as follows:
Years | Percentage with 4 years of high school | Percentage with 4 years of college or more
------------|-----------------------------------------|------------------------------------------------
1960 | 39.5% | 9.7%
1970 | 51.9% | 13.5%
1980 | 67.3% | 20.1%
1990 | 77.7% | 24.4%
2000 | 84.2% | 27.8%
2004 | 84.8% | 29.4%
b) The matrix for the educational attainment of females can be written as follows:
Years | Percentage with 4 years of high school or more | Percentage with 4 years of college or more
------------|-------------------------------------------------|-------------------------------------------------
1960 | 42.5% | 5.8%
1970 | 52.8% | 8.1%
1980 | 65.8% | 12.8%
1990 | 77.5% | 18.4%
2000 | 84.0% | 23.6%
2004 | 85.4% | 26.1%
c) To find the difference in educational attainment between males and females since 1960, we need to subtract the corresponding values from the matrices in parts a) and b).
The matrix showing the difference in educational attainment between males and females since 1960 can be calculated as follows:
Years | Difference in Percentage with 4 years of high school | Difference in Percentage with 4 years of college or more
------------|------------------------------------------------------|--------------------------------------------------------------
1960 | (39.5% - 42.5%) | (9.7% - 5.8%)
1970 | (51.9% - 52.8%) | (13.5% - 8.1%)
1980 | (67.3% - 65.8%) | (20.1% - 12.8%)
1990 | (77.7% - 77.5%) | (24.4% - 18.4%)
2000 | (84.2% - 84.0%) | (27.8% - 23.6%)
2004 | (84.8% - 85.4%) | (29.4% - 26.1%)
Simplifying the calculations, we get:
Years | Difference in Percentage with 4 years of high school | Difference in Percentage with 4 years of college or more
------------|------------------------------------------------------|--------------------------------------------------------------
1960 | -3.0% | 4.1%
1970 | -0.9% | 5.4%
1980 | 1.5% | 7.3%
1990 | 0.2% | 6.0%
2000 | 0.2% | 4.2%
2004 | -0.6% | 3.3%
Therefore, the matrix showing the difference in educational attainment between males and females since 1960 is:
Years | Difference in Percentage with 4 years of high school | Difference in Percentage with 4 years of college or more
------------|------------------------------------------------------|--------------------------------------------------------------
1960 | -3.0% | 4.1%
1970 | -0.9% | 5.4%
1980 | 1.5% | 7.3%
1990 | 0.2% | 6.0%
2000 | 0.2% | 4.2%
2004 | -0.6% | 3.3%