Math Problem Statement
The scatterplot shows the median starting salaries and the median mid-career salaries for graduates at a selection of colleges. Complete parts (a) through (e) below.
Mid-Careerequals=negative 8075−8075plus+1.9881.988
Start Med
304050607080255075100125150175Start Median Salary (thousands of $)Mid-Career Salary (thousands of $)
A graph has a horizontal axis labeled "Start Median Salary (thousands of dollars)" from 30 to 80 in increments of 10 and a vertical axis labeled "Mid-Career Salary (thousands of dollars)" from 25 to 175 in increments of 25. A line ascends from left to right and forty points are scattered around the line as it ascends, with approximately half of the points above the line and half below the line. The line travels through the following points: (30, 52), (40, 71), (50, 91), (60, 111), (70, 131) and (80, 151). All points are approximate.
Question content area bottom
Part 1
a. As the data are graphed, which is the independent and which the dependent variable?
The independent variable is
median starting salary
and the dependent variable is
median mid-career salary.
Part 2
b. Why do you suppose median salary at a school is used instead of the mean?
A.
Salary distributions are usually bimodal, making the median a more meaningful measure of center.
B.
Salary distributions are usually bell-shaped, making the median a more meaningful measure of center.
C.
It is easier to calculate the median for a salary distribution instead of the mean.
D.
Salary distributions are usually skewed, making the median a more meaningful measure of center.
Your answer is correct.
Part 3
c. Using the graph, estimate the median mid-career salary for a median starting salary of
$ 40 comma 000$40,000.
The median mid-career salary for a median starting salary of
$ 40 comma 000$40,000
is about
$71,00071,000.
(Round to the nearest thousand as needed.)
Part 4
d. Use the equation to predict the median mid-career salary for a median starting salary of
$ 40 comma 000$40,000.
The median mid-career salary for a median starting salary of
$ 40 comma 000$40,000
is about
$enter your response here.
(Round to the nearest dollar as needed.)
Solution
We are given the equation for predicting the median mid-career salary:
Step 1: Substitute for the Start Median Salary
Step 2: Compute the value
Step 3: Round to the nearest dollar
Thus, the predicted median mid-career salary for a median starting salary of $40,000$ is $71,445$.
Would you like a breakdown of any step?
Related Questions:
- How do you determine if a variable is independent or dependent?
- Why is the median more robust against skewed distributions than the mean?
- How can we check if the regression equation is a good fit for the data?
- What is the significance of the slope in this regression equation?
- How would an outlier affect the accuracy of this prediction?
Tip: Always compare predicted values with actual values from the graph to assess the reliability of your regression model.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Scatterplots
Median Calculation
Prediction with Equations
Formulas
Mid-Career Salary = -8075 + 1.988 * Start Median Salary
Theorems
Regression Line Interpretation
Prediction using Linear Equations
Suitable Grade Level
Grades 9-12
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