Annual Salaries and Gender
Student Guide
Annual Salaries and Gender
According to a recent New York Times article, more than thirty percent of American adults hold
bachelor’s degrees. In the early 1980s, women first started to outnumber men in college
enrollment. Since the mid-1990s, women have earned more bachelor degrees than men. Does this
mean that annual salaries have followed suit? In this task, you’ll apply what you’ve learned in this
unit to answer this question.
Directions
Complete each of the following tasks, reading the directions carefully as you go. Be sure to show all work
where indicated, including inserting images of graphs. Be sure that all graphs or screenshots include
appropriate information such as titles, labeled axes, etc. If your word processing program has an equation
editor, you can insert your equations here. Otherwise, print this activity sheet and write your answers by
hand.
In addition to the answers you arrive at, you will be graded based on the work you show, or your solution
process. So, be sure to show all of your work and answer each question as you complete the task. Type
all of your work into this document so you can submit it to your teacher for a grade. You will be given
partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions as to how you are to submit your work. You may be asked to
upload the document, e-mail it to your teacher, or hand in a hard copy.
Now let’s get started!
Step 1: Finding regression equations for the relationship between time and degrees
earned.
Below is a table depicting the number of US citizens, in thousands, who earned a bachelor degree for
each year since 2000.
Year
00
01
02
03
04
05
06
07
08
Male
530
532
550
573
595
613
631
668
681
Female
708
712
742
775
804
826
855
895
918
a. Use the regression calculator or another tool of your choice to create a scatter plot of the data
for men, where the independent variable is the year since 2000 and the dependent variable is
the number of people (in thousands). Take a screenshot of your scatterplot and paste it
below. If your graph does not include labels, then include a description of what the axes
represent.
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Student Guide (continued)
The x-axis is the independent variable and it represent the number of years since 2000. The
y-axis is the dependent veriable and it represents the number of US citizens(in thousands)
who earned a bachelor degree.
b. Use your calculator to find the regression line y = mx + b for men where x is the number of
years since 2000 and y is the number of men. Complete the regression equation below.
M(x) = 20.233x+516.067
c.
Repeat the above steps with the data for women.
Insert a screenshot of the scatterplot for women below.
Look at scatterplot 1.docx
Complete the regression equation below.
F(x) = 28.678x+685.99
Step 2: Interpreting the regression equations for the relationship between time and
degrees earned.
a. Often, social changes, such as education trends, show linear relationships. How well
does a linear model fit the data in this problem? Justify your answer in terms of the
scatterplots and in terms of the data that the regression calculator gives.
Both scatterplots show a positive correlation. For men, 𝑟 ≈ .991 and, for women, 𝑟 ≈ .983. The
linear model fits the data moderately well, because .991 and .983 are extremely near to 1.
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Student Guide (continued)
b. Using proper units, state the slopes for the functions M and F.
Slope of M: 20.233
Slope of F: 28.687
c.
Explain what these slopes represent in terms of Americans earning bachelor degrees.
Every year, there is a sharper increase of females earning bachelor degrees than males.
Step 3: Solving a system of equations to make comparisons between men and women
earning degrees.
a. The functions M and F form a system of linear equations. Use your graphing calculator to find the
solutions to this system graphically. Insert a screenshot of your graph below.
b. The solution of the system is: (-20.12, 108.96)
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Student Guide (continued)
c.
Solve the system again using any algebraic method, such as substitution or elimination. Show
your work step-by-step with clear notation. Make sure your answer matches the answer you
found in the previous problem.
y = 20.233x+516.067
y = 28.678x+685.99
Substitute and Solve:
20.233x+516.067=28.678x+685.99
-20.233x
-20.23x
516.067=8.445x+685.99
-685.99
-685.99
-169.923=8.445x
----------- --------8.445
8.445
x=-20.12113677
Substitute -20.12113677 back in for x and solve for y:
y=20.233(-20.12113677)+516.067
y=-407.11096027+516.067
y=108.95603973
Solution: (-20.12, 108.96)
d. Interpret the solution to the system in terms of Americans earning bachelor degrees. Recall the
opening paragraph: “In the early 1980s, women first started to outnumber men in college
enrollment. Since the mid-1990s, women have earned more bachelor degrees than men.” State
whether or not you think your results from Steps 3a-3c support the opening paragraph. Justify
your reasoning. If the results do not support it, explain why this might be.
3a-3c has supported the opening paragraph. -20 would signify 20 years ago, which was 1980.
The solution to the system of equations show that in 1980 there was the same amount of women
as there were men earning bachelor degrees. The first sentence states early 1980’s, so women
did not start to out number men exactly in 1980, but a little bit after. This is shown in the graph; by
1981, an estimated 141 women were earning bachelor degrees, while an estimated 131 men
were earning bachelor degrees. By 1995, 414 men and 542 women were earning bachelor
degrees. The graph shows that women have been earning mor bachelor degrees ever since.
Step 4: Extrapolating to predict the number of degrees earned by men and women.
a. Use the models for M and F to predict the number of degrees that will be earned by men
and women in the year 2015.
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Student Guide (continued)
The number of degrees earned by men = 819
The number of degrees earned by women = 1116
Step 5: Using data from a specific town to write equations and draw conclusions about
degrees earned.
In Springfield, a specific town in the US, 6 women and 25 men earned bachelor degrees in 2000. In
2010, however, 391 women and 410 men in that town earned bachelor degrees. Assume that the
rate of change was constant between 2000 and 2010.
a. Without using regression, write a system of equations that model the number of bachelor degrees
earned by men and women in Springfield as a function of x, the number of years since 2000.
Show your work.
Equation for Springfield’s men:
X=number of years since 2000
Y= number of men
Use point slope form to find slope:
25-410=m(0-10)
-385=m(-10)
-385=-10m
------ -------10
-10
38.5=m
Use y=mx+b and substitute in what you know:
b=y-intercept=25
Answer: y=38.5x+25
Equation for Springfield’s women:
X=number of years since 2000
Y=number of women
Use point slope form to find slope:
6-391=m(0-10)
-385=m(-10)
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Student Guide (continued)
-385=-10m
------
------
-10
-10
38.5=m
Use y=mx+b and substitute in what you know:
b=y-intercept=6
Answer: y=38.5x+6
b. When, if ever, will the number of women earning bachelor degrees equal the number of men
earning bachelor degrees in Springfield? Justify your answer using appropriate mathematics
vocabulary.
Approximately, the number of women earning bachelor degrees will never equal the number of men
earning bachelor degrees, because the system of equations modeling the number of men and women
earning bachelor degrees are parallel and have no solution. Both equations have the same slope and
different y-intercepts, so they will never intersect, which shows that there will never be the same amount
of women and men earning bachelor degrees.
Step 6: Analyzing trends between degrees earned and salaries.
The table below shows the median annual salaries in the United States by gender. Use the skills from this
lesson to correlate trends in the US from 2000 to 2010 in the number of people who received a bachelor
degree to annual salaries by gender.
Men
Women
Total
Percentage
women to men
01
$34,944
$26,572
02
$35,308
$27,508
$31,616
77.9%
03
$36,140
$28,704
$32,240
79.4%
04
$37,076
$29,796
$33,176
80.4%
05
$37,544
$30,420
$33,852
81.0%
06
$38,636
$31,200
$34,892
80.8%
07
$39,832
$31,928
$36,140
80.2%
08
$41,496
$33,176
$37,544
79.9%
09
$42,588
$34,164
$38,428
80.2%
10
$42,848
$34,788
$38,844
81.2%
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Student Guide (continued)
a. Assuming a linear relationship between year and salaries by gender, determine when the median
annual salary for women will exceed men. Justify your answer. Include in the discussion the
regression analysis you performed.
b. Based on the answer you found in the above step, provide an argument pro or con to the
statement “As the number of women exceed men in the number of bachelor degrees received,
expect there to be a corresponding change in the median annual salaries for each gender.”
Sources:
http://www.nytimes.com/2012/02/24/education/census-finds-bachelors-degrees-at-record-level.html
http://www.good.is/post/women-now-earning-more-bachelor-s-and-graduate-degrees-than-men/
Source: http://maamodt.asp.radford.edu/HR%20Statistics/Salary%20by%20Sex%20and%20Race.htm
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